Ch4_EisenbergAmandaE

= = toc Section 1

Initial Research **Possessed:** the ride features zero-gravity and cobra rolls and corkscrews. A cobra roll takes the rider upside down twice, and a corkscrew resembles a typical loop that has been stretched out. In a corkscrew, riders are angled at 90 degrees horizontally from the incoming track. **Talon:** the ride is floorless and uses a zero-gravity roll and an Immelman loop. The former places the center of gravity on the rider's heart to make him feel weightless, and the latter is an inverted loop where the rider's head is perpendicular to the track below him. http://en.wikipedia.org/wiki/Immelmann_loop#Immelmann_loop

What Do You See? Someone is being pushed in a wheely chair at various velocities and accelerations like they are on a roller coaster.

What Do You Think? The parts that have the greatest amount of acceleration and turns creates the loudest screams, like the loops.

Physics Talk **Scaler:** a quantity that has magnitude (size/amount), but no direction **Displacement:** the difference in position between a final position; it depends only on the endpoints, not the path; displacement is a vector quality, it has magnitude (size) and direction **Vector:** a quantity that has both magnitude (size/amount) and direction **Speed:** distance traveled divided by the time elapsed; speed is a scaler quantity, it has no direction **Velocity:** displacement divided by the time elapsed; velocity is a vector quantity, it has magnitude and direction **Acceleration:** The change in velocity divided by the time elapsed; acceleration is a vector quantity, it has magnitude and direction

Checking Up 1) Displacement is the difference in position between a final position, whereas distance is the total difference between the start and the final positions. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) 0 km because you wound up where you started <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) Speed is distance divided by time whereas velocity is displacement divided by time. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) Total change in velocity over total change in distance = acceleration

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">What Do You Think Now? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">The downward hills cause the most amount of acceleration, therefore producing the loudest scream. During the investigation, I felt the most jolted when experiencing quick accelerations.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;"> <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) The acceleration around curves and drops creates the largest thrills.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3A) La Paz in Bolivia has the greatest speed; it travels the greatest distance <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3B) v = d/t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">v = 40,000 / 24 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**v = 1666 2/3 m/s** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3C) It has a high speed but because of its consistency it does not feel like you are going fast

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) a = vf - vi / t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">a = 16 - 4 / 3 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**a = 4 m/s^2**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5A) Speed <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5B) Velocity <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5C) Acceleration <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5D) Distance <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5E) Displacement

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">6) v = d/t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">v = 0.1/2 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**v = .05 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">7) v = d/t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">0.05 = .05/t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">**t = 1 s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">8) a = v/t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">a = vf - vi / t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">a = 25-0 / 10 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**a = 2.5 m/s^2**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">10A) To make it more enjoyable for younger kids, I would alter the angle to make it less extreme for the kids. Anything to steep or scary would be too scary. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">10B)

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 2 ** =

<span style="font-size: 16px; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You See? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">The people around the bend are sleeping, while the people going down the hill are screaming.

<span style="font-size: 16px; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">The steel roller coaster has the biggest thrill because of its steeper angle in comparison to the wooden roller coaster's 60 degree angle.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics Talk <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**GPE:** The energy a body possesses as a result of its position in a gravitational field <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**KE:** The energy an object possesses because of its speed <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Joule:** The unit for energy <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Mechanical Energy:** The sum of GPE + KE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Bar Chart:** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Checking Up <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) When lengthening the incline, the ball will have a faster velocity at the bottom of the ramp. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) Because GPE = mgh, any increase in a variable will increase the amount of energy in the object's potential energy. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) The same goes for kinetic energy as it does for GPE. However, velocity is the only variable that is squared, so it carries more weight than the rest. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) The cart starts with GPE and that turns into KE when it is released down the ramp. Because mechanical energy is GPE + KE, then the energy remains the same. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5) KE + GPE(bottom) = KE + GPE(top) 3/4(40,000)(Kinetic Energy) + 1/4(40,000)(GPE) = 0 + 40,000  **KE = 30,000 J**

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">What Do You Think Now? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">When the carts start at the same height, their velocity and final magnitude are the same. Regardless of the incline, the carts will have the same velocity when traveling the same distance; however, the shorter track is going to be the one with the cart to finish first. This proves that the bigger the acceleration, the bigger the thrill.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) The speeds are both the same because the distance does not change. However, graph B would be faster if friction played a role.

<span style="border-collapse: separate; color: #800080; font-family: Arial,Helvetica,sans-serif;">3)
 * 60,000 || 0 || 60,000 ||
 * 0 || 60,000 || 60,000 ||
 * 30,000 || 30,000 || 60,000 ||
 * 15,000 || 45,000 || 60,000 ||

5) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">4 + 6) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">
 * 300(10)(25) = 75000 || 0 || 75,000 ||
 * 0 || 75,000 || 75,000 ||
 * 37,500 || 37,500 || 75,000 ||
 * 300(10)(5) = 15,000 || 60,000 || 75,000 ||

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">8) KE and GPE both have mass in their equations, so when set equal to one another the masses cancel out; any system that uses gravity doesn't need mass to be solved.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">9A) Point B showcases where the energy has changed from the highest GPE to the highest KE. The acceleration is maximized here, but as it goes back up the hill, the object will lose its KE but gain GPE proportionally. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">9B) Ignoring friction, points B and G are the same height off of the ground and therefore have the same GPE and KE. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">9C) Point D is where the object moves the fastest because of its low GPE and high KE.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 3 =

<span style="font-size: 16px; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You See? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Students are playing with spring toys and measuring its vertical distance.

<span style="font-size: 16px; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Roller coaster carts usually need to go up a hill, so they either get pulled or move up a track. Carts full of people need more energy to lift it because the mass is now heavier.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics Talk <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Spring Potential Energy:** the energy stored in a spring due to its compression or stretch

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Checking Up <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) That energy is then translated into kinetic energy once it is popped upward. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) Energy cannot be created or destroyed, so the 2 J of SPE is transferred as 2 J of KE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) Once again, energy cannot be created or destroyed. That energy is now 2 J of GPE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) SPE = 1/2(k)(x^2)

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">5) The cart moves up a hill and at its peak it has a maximum GPE. Once that energy is transformed into KE, it then can move up and down hills. However, the maximum energy has been reached, so the next hill cannot exceed the previous. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">6) The cart has a certain amount of kinetic energy at the start of the roller coaster. To go up and down hills, the cart needs to maintain a certain energy to do so; when the cart does not have the amount, it slows down until it finally will come to a stop. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">7) GPE = mgh <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">= 300(9.8)(15) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">= **44,100 J**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">8A) KE = 1/2m(v^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">= 1/2(400)(15^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">= **45,000 J** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">8B) The GPE will be 45,000 J of energy if the kinetic energy is 0 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">8C) 45000 = 400(9.8)h <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">**h = 11.48 m**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">9) The GPE is maximized at its highest point, so when rising it's GPE is increasing and when it falls its decreasing. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">10) All three people will have the same GPE in the end, but whoever walks on route A will gain the most GPE the fastest.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">11A) GPE = KE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">0.02(9.8)(0.4) = 1/2(0.02)(2.7^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**0.0784 = 0.0729** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**The values are very similar.**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">11B) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">mgh + 1/2m(v^2) = SPE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">0.02(9.8)(0.4) + 1/2(0.02)(2.7^2) = SPE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">0.0784 + 0.0729 = SPE

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">11C) The height would reach 1/3 of its original height.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">12A) GPE = EPE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">mgh = 1/2k(x^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">300(9.8)(18) = 1/2(4)(x^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">52920 = 2x^2 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">26460 = x^2 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">**x = 162.67 m**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">12B) GPE = EPE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">mgh = 1/2k(x^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">400(9.8)(18) = 1/2(4)(x^2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">70560 = 2x^2 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">35280 = x^2 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">**x = 187.83 m**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">13) EPE = KE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">1/2k(x^2) = KE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">1/2(40)(.3^2) = KE <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**KE = 1.8 J**

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">What Do Y u Think Now? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">With most roller coasters, a chain drags the carts up a hill to reach a certain height in order to fulfill the needed amount of energy to ride the track. The amount of energy needed to lift the cart fully depends on the mass of the cart with the maximum weight of all of the passengers. This is why roller coasters have weight limits, to ensure safety when reaching maximum GPE.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 4 =

<span style="font-size: 16px; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You See? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">The astronauts on the moon are on a roller coaster, but do not seem to be having fun. However, Jupiter's roller coaster has them screaming in delight.

<span style="font-size: 16px; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Gravity points to the center of the Earth, regardless of what direction you are facing. Liquids that drain in Australia turn the opposite way than in America due to the change in gravity.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics Talk <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Gravitational Field:** the gravitational influence in the space around a massive object <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Inverse-square Relationship:** the relationship between the magnitude of a gravitational force and the distance from the mass. This also describes how electrostatic forces depend on the distance from an electrical charge <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Newton's Law of Universal Gravitation:** all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bodies increases. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Gravity:** the force of attraction between the two bodies due to their masses

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Checking Up <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) Gravity pulls towards the center of the earth. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) Gravity is stronger where the lines are closest together whereas the further away from the center, the weaker the gravity. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) The gravity is then cubed. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) The moon and its orbit is held together by the same gravity <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5) The shape of the orbit around the sun is elliptical.

Physics Plus <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) **a = (v^2)(r)** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) v = d/t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">(2pi)(3.84 x 10^8) / 2440800 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**v = 998.51 m/s** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) a = v^2 / r <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">a = 998.51^2 / (3.84 x 10^8) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**a = 0.0025 m/s^2**

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) 1/25

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2A) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">1/4 of the force <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">2B) 1/9 of the force <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">2C) 1/16 force.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) Every mass has gravitational force, so the GPE will always be present. This is a secure fact, so there is no reason to distrust it.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) Both values of GPE and KE (when set equal to one another) are very similar. The only slight difference is that the point at the top will have a miniscule amount less than the cart at the bottom because of the difference in height. The closer to the earth, the more gravity it will have.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5A) The water sits on the Earth. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5B&C) More water on the side facing the moon because the water is attracted to the moon's pull

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">6A&B) Water's polarity has a gravitational pull, and the fish also has GPE. This keeps the water and the fish grounded.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">7A) 1/4 of the force. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">7B) 1/9 of the force. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">7C) 1/16 of the force. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">7D) 4x the force

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">8A) Doubles <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">8B) Triples <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">8C) Quadruples <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">8D) Half

9A) Quadruples 9B) 9x the force 9C) 16x the force 9D) 1/4 of the force

10A) Doubles 10B) 9x the force 10C) 6x the force

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">What Do You Think Now? Attraction between two masses accounts for gravity's direction. Because everything is pulled towards the center of the Earth, people do not feel upside down regardless of their geographical location. Gravity acts on all masses, so the ground is attracted to the center of the earth, and we are attracted to the ground.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 5 = = What Do You See? = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">The same piece of meat is being weighed by 2 different scales - one at a deli and one at a lab. =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">** What Do You Think? ** = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">A scale that measures an elephant would not be able to make sense of the small mass of the canary and vice versa. A scale works by a mass stepping on it and stretching the coil. The distance is measured and recorded for the person to see their weight, also in combination with gravity.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics Talk <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Hooke's Law:** Fs = -kx <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">(F = force of spring in N; k = spring constant in N/m; x = stretch distance in m)
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Force is opposite distance
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Slope is the spring constant



<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Checking Up <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) The spring will be stretched 5x its original to show the heavier mass exerted onto it. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) The spring constant is the slope of the stretch and force of a spring <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) The weight in Newtons is equal to the mass in kg multiplied by gravity. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) That number needs to be multiplied by gravity's force in order to find someone's weight using a bathroom scale.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1A) w = mass(gravity) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">w = (100)(9.8) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**w = 980 kg** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1B) w =mass(gravity) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">w = 10(9.8) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**w = 98 kg** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1C) w = mass(gravity) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">w = 60(9.8) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">**w = 588** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2A) 130(4.4) = **572 N** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2B) 1000(4.4) = **4400 N** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2C) 50(4.4) = **2260 N** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;"> <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3D) The slope is 6.7441, and that shows the spring constant.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) F(s) = -kx <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">12 = -k(.03) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">400 = -k <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**k = -400 N/m**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5) The force and the spring stretch are positively correlated; when one increases or decreases, so does the other. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">6) The higher the spring force constant, the more force is needed to straighten it out. For example, a 15 N/cm spring is harder to stretch than a 10 N/cm spring.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">7) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">F(s) = -kx <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">3 = -k(.02) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">150 = -k <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**k = -150 N/m**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">8) A spring scale compresses when a weight is pressed upon it, and the spring moves an arrow to show the weight. The tighter the compression, the heavier the weight.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">What Do You Think Now? <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">The calibration for the two very different objects varies too much to use the same scale. As for the spring force, the constant is proportional to the distance it stretches, and therefore moves the arrow to the designated number to determine one's weight.

= = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 6 ** = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">** What Do You See? ** = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">The fat guy is pushing down on the scale while the air is pushing down on his box. The mouse is being pushed upward but is applying little force to its scale.

=<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think? = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">I do think your weight changes when you are on a roller coaster at certain spots. When I've ridden roller coasters in the past, I feel lighter at the top and then as I'm accelerating downward, much heavier.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics Talk <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">**Newton's first law:** object at rests stays at rest, or in motion stays in motion, unless acted on by unbalanced force <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">**Newton's second law:** unbalanced force creates an acceleration <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">v <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">> <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">> t > f <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">a
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">The bigger force is in the same direction as acceleration
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">To do this draw motion map and free body diagram
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">increasing right

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">v <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">< <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">< f > t <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin: 0px;">a
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">increasing left

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Checking Up <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) a = f/m shows that when an object is moving at constant speed there is zero acceleration, so there are no net forces acting on it. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2 & 3) When the roller coaster accelerates upward, there is a net force acting on the object. This makes you feel heavier than you actually are, and the reading on the scale will verify this. Because there is a net force acting on you, it puts more force on the scale. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) Because you are in free fall, you will feel less than you normally weigh. Because everything in the elevator is in free fall as well, there is no force connecting the scale to yourself, so the scale would read zero. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5) Air resistance slows down rain drops

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">1A) vf = vi + at <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">vf = 9.8(2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**vf = 19.6 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">1B) vf = vi + at <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">vf = 9.8(5) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**vf = 49 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">1C) vf = vi + at <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">vf = 9.8(10) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**vf = 98 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">2A) vf = vi +at <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">vf = 1.6(2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**vf = 3.2 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">2B) vf = vi + at <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">vf = 1.6(5) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**vf = 8 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">2C) vf = vi + at <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">vf = 1.6(10) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**vf = 16 m/s**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">4)
 * **Motion of the Elevator** || **Acceleration (up, down, zero)** ||  || **Relative Scale Reading (greater, less or equal to weight)** ||
 * At rest, bottom floor || zero ||  || equal ||
 * Starting at Rest, Increasing Up || up ||  || greater ||
 * Continuing to move, Constant Up || zero ||  || equal ||
 * Slowing down to top floor, Decreasing Up || down ||  || less ||
 * At rest, top floor || zero ||  || equal ||
 * Starting at rest, Increasing Down || down ||  || less ||
 * Continuing to move, Constant Down || zero ||  || equal ||
 * Coming to a stop on the ground floor || up ||  || greater ||

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">5) change in force = ma

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">6) It will appear heavier than the actual weight because the normal force is greater than weight.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">7A) You will feel lighter than normal and the scale will read a lighter number. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">7B) change in force = ma <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">N - mg = ma <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">N = ma + mg <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">N = 50(-1.5) + 50(9.8) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">N = - 75 + 490 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**N = 415 N**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">8A) w = mg <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">50(9.8) = **490 N** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">8B) Net force = ma <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Net force = 50(2) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">100 + 490 = **590 N** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">8C) N - w = ma <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">N = w = **490 N**

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">9) When there is no acceleration, there is normal weight. When there is acceleration pointing downwards, the net force points down and there is no apparent weight. When there's acceleration upward, the net force also points up and therefore there is a heavier apparent weight.

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">10) Our roller coaster targets extreme riders, and the thrills come from fast acceleration. Sharp turns, quick acceleration changes, and steep drops keep the rider excited.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think Now? ** = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">No your actual weight does not change on a roller coaster, however, you may feel heavier or lighter at certain points. When you accelerate upward, you will feel heavier whereas accelerating downward makes you feel lighter.

= = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 7 ** = =<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> What Do You See? = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">The people look like they are falling off the track because the cart wants to continue moving tangent from the curve. =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think? ** = <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">The cart is moving at such a fast speed that it can continue around the loop without causing people to fall out. There is centripetal force keeping the cart moving around the loop.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics Talk <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Normal force:** the force acting perpendicular to the surface <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Centripetal force:** any force directed toward the center that causes an object to follow a circular path at constant speed <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Centripetal acceleration:** the acceleration directed toward the center of a circle experienced by an object traveling in a circular path at constant speed <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">**Uniform Circular Motion:** tangential speed, usually constant
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">if Ac = 0, then moving in a straight like
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Change in centripetal force = m(v^2) / r
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">v^2 / r = centripetal acceleration
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Radius increases, Centripetal force decreases
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Mass increases, Centripetal force increases
 * <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">Velocity increases, Centripetal force decreases





<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Checking Up <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">1) Centripetal force. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">2) Yes. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">3) Weight and normal. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">4) Normal. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 13px; line-height: 19px; margin: 0px; padding: 0px;">5) The mass has a direct relationship, the radius has a indirect inverse, and the centripetal acceleration has a squared inverse.

<span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 16px; line-height: 24px; margin: 0px; padding: 0px;">Physics To Go <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">1) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">2A) Friction <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">2B) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">The car will move tangent to the circle <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">6A) The velocity remains constant at 20 m/s <span style="color: #800080; font-family: Arial,Helvetica,sans-serif;">6B) Yes, the direction does. <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">6C) Change in velocity = v2 - v1 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">= v2 + (-v1) <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">20^2 + 20^2 = SQRT800 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">tan(pheta) = 20/20 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">pheta = **45 degrees** <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-weight: normal; margin: 0px; padding: 0px;"> 28.3 m/s at 45 degrees North West

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">7) Ac = v^2 / r <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">= 20^2 / 200 <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; margin: 0px; padding: 0px;">**Ac = 2 m/s**

10) **Fast**  **Slow**  13A) They seem heavier 13B) It is impossible to tell if weight is greater than normal force, but inertia makes it feel heavier 13C) They appear heavier 13D) They seem heavier 13E) No change.
 * || Required Centripetal Force || Force of Gravity (weight) || Normal Force ||
 * Top of loop || 4,000 N || 500 N || 3,500 N ||
 * Bottom of loop || 6,000 N || 500 N || 6,500 N ||
 * || Required Centripetal Force || Force of Gravity (weight) || Normal Force ||
 * Top of loop || 800 N || 500 N || 300 N ||
 * Bottom of loop || 2,800 N || 500 N || 3,300 N ||

14A) Up 14B) Down 14C) Up 14D) Up  14E) No force  14F) Sideways 14G) Sideways

=<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> What Do You Think Now? = = ** Due to centripetal acceleration, you feel heavier when you go around a loop, but the acceleration is directed towards the middle. This holds you in place, and because the acceleration is greater than gravity, you can never be in free fall. ** =

= = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> Section 8 = What Do You See? It looks like people are making a large effort to push a cart up the hill to reach maximum GPE

What Do You Think? Because GPE remains the same, the amount of energy is just transferred but never changed.

Physics Talk **Work:** the product of displacement and the force in the direction of the displacement; the energy transferred to an object **Power:** the work done divided by the time elapsed; the speed at which work is done and energy is transferred **Watt:** the SI unit for power; 1 W = 1 J/s =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">** Checking Up ** = 1) GPE is at the top 2) The work due to pulling up the cart is GPE at the top 3) The power lessens over time 4) It's converted to work or EPE 5) Watt
 * Power is the rate of the energy dissipation (uses up)
 * How to stop a roller coaster
 * 1) Compression of spring
 * 2) Thermal energy

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Physics To Go ** = 1A) All of the energy at the top is GPE 1B) GPE / h  1C) All of it. GPE = EPE  1D) 1/2kx^2 1E) GPE 1F) When you just touch the spring you begin to slow down

2A) There is no acceleration. 2B) w = fd  w = 60(0.5) **w = 30 J** 2C) w = fd w = 40(75)  **w = 3000 J**  2D) w = fd  w = 500(0.7) **w = 350 J**

3) Electrical energy is costly and streams directly to the object; it isn't the type of energy that is required to stay within a system.

4) It would have to be heavier so the energy could bring the cart to the top. In order to maximize GPE, more power would be needed to push the cart.

5A) w = GPE w = 10000(20)  **w = 200,000 J**  5B) p = w / t  p = 200,000 / 150 **p = 1333.3 J**

6) Work is needed to lift the cart to the top, where the energy is converted to GPE. On the way down, that energy is turned into KE. While the cart goes through a vertical loop, KE and GPE are transferred between each other. KE remains in play during the rest of the ride until EPE creates a break to stop the cart at the end of the ride. = = =<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think Now? = The incline of a hill only changes the amount of power, but never the amount of work needed. It is only harder to walk up a steep incline because it involves utilizing more power.

= = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 9 ** =

What Do You See? The girl is filling up her paper with equations to find the amount of energy. It's easily calculable, whereas the boy needs more information to determine the force needed for the roller coaster. =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think? ** = The parts where there are sharp turns and changes in accelerations make the ride the most fun and exciting.

Physics Talk

Checking Up 1) Pythagorean Theorem is needed to add vector quantities.  2) Energy is a scaler and force is a vector 3) We would need to know the GPE, KE, and the total energy. We can use them to find height and velocity. 4) No, the path does not change the amount of energy 5) Work is needed to change the amount of energy

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Physics to Go ** = 1) 2) The accelerations will be different although their velocities remain the same. This is due to a longer track accelerating slowly but building up speed, while the shorter track accelerates more quickly but only does it for so long. If the tracks start out at the same height and end in the same place, the kinetic energy and the velocity will be the same.

3A) Distance - Scaler 3B) Displacement - Vector 3C) Speed - Scaler 3D) Velocity - Vector 3E) Acceleration - Vector 3F) Force - Vector 3G) KE - Scaler 3H) PR - Scaler 3I) Work - Vector

4A) Scaler 4B) Vector 4C) Scaler 4D) Vector

5) When given a height or velocity, it is always best to look for the x factor in terms of energy. When you are given specifics like a roller coaster at 20 meters in height that weighs 5 kg, you are able to find the velocity at the end of the track. The height is used for GPE whereas the KE is used to find the speed at the bottom of the track. In order to find net force, you need to draw a free body diagram and show where the forces are pointing at.

6-7A)

7B) The total energies are the same at both points because the total energy is the same in each particular system. The energy is just transferred from GPE to KE. 7C) The KE starts at the same height and therefore is the same. 7D) The height is the only other element is the only thing that determines GPE and then that number is transferred into KE.

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think Now? ** = When there are sharp turns from a small radius, the whipping feeling is much stronger than wider turns. The whipping showcases a greater acceleration and creates a more thrilling ride.

= = = = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Section 10 ** =

What Do You See? There are hundreds of carts falling off tracks and into lakes, and people are flying out.

What Do You Think? The aspect of possible death is fascinating and definitely increases the risk of riding a roller coaster. The occurrence of this happening is so slim that you may be worried about it for a little bit but by the 3rd ride you completely disregard it. However, if 1 out of every 2 riders died, absolutely no one would ride roller coasters except those who are suicidal.

Physics Talk = = =<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Checking Up = 1) 4 Gs is the maximum acceleration. 2)
 * Acceleration cannot exceed 4 Gs or 40 m/s.
 * Free fall = 1 G
 * Centripetal acceleration = v^2 / r
 * Centripetal force required in Newton's 2nd Law: f(net) = mv^2 / r
 * The velocity cannot exceed 40 m/s
 * The Gs need to be in between 1 & 4 Gs or else the cart would be in free fall.

3) At the bottom of the horizontal loop 4) At the bottom of the vertical loop

=<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;"> Physics To Go = <span style="color: #800080; font-size: 13px; font-weight: normal; line-height: 19px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">1) The engineers need to make sure that the acceleration is under 4 Gs, and that the top of the loop must be bigger than 1 G to avoid free fall.

2A) mgh + 1/2m(v^2) = mgh (9.8)h + 1/2(20^2) = (9.8)h  **20 = h**

2B) a(c) = v^2 / r a(c) = (20^2) / 12  **a(c) = 33 m/s^2**

2C) Yes it is 3.4 Gs

2D) a(c) = = v^2 / r 39.6 = v^2 / 12  **v = 22 m/s**

2E) a(c) = v^2 / r 39.6 = v^2 / r  **v = 17 m/s**

3A) a(c) = v^2 / r a(c) = 25^2 / 10  **a(c) = 63 m/s^2**

3B) No, it's 6.3 Gs

4A) mgh = 1/2m(v^2) 9.8(50) = 0.5(v^2)  **v = 31 m/s**

4B) a(c) = v^2 / r a(c) = 31^2 / 10  **a(c) = 96 m/s^2**

4C) KE = GPE(1) - GPE(2) KE = 50(9.8) - 20(9.8)  **KE = 294 J**  KE = 1/2(v^2)  294 = 1/2(v^2)  **v = 24 m/s**

4D) ac = v^2 / r ac = 24^2 / 10  **ac = 58 m/s^2**

4E) The bottom of the loop exceeds the 4G cap and it's acceleration greatly surpasses it.

5A) ac = v^2 / r 9.8 = v^2 / 8  **v = 8.9 m/s**

5B) GPE = KE + GPE mgh = 1/2m(v^2) + mgh  9.8h = 1/2(8.9^2) + 9.8(16)  **h = 20.1**

6) ac = v^2 / r ac = 12^2 / 18  **ac = 8 m/s^2**

6B) Fc = mv^2 / r Fc = 900(12^2) / 18  **Fc = 7,200 N**

6C) The friction from the wheels on the track

7A) ac = v^2 / r ac = 20^2 / 15  **ac = 26.7 m/s^2**

7B) Fc = m(v^2) / r Fc = 900(20^2) / 15  **Fc = 24,000 N**

7C) The roller coaster can use up to 25,000 N, and the coaster in 7B is 1,000 N under the maximum.

8A) No, mass is not a factor in centripetal acceleration (v^2 / r). 8B) The mass will be omitted because the speed does not change. 8C) The normal force will increase when the weight increases, and the track's strength needs to increase with the enlargement of the weight.

=<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">Physics Plus = <span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">





= = =<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="font-size: 16px; font-weight: normal; line-height: 24px; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">What Do You Think Now? ** = The loops and hills are the most dangerous because if they don't have enough or too much Gs, the carts can be in free fall or simply fly off the track. Roller coaster engineers need to be aware to this pertinent information to keep riders safe.