Physics Midterm-An amusement park ride consists of a cart with some riderS
Subject: Physics   / General Physics
Question
6. An amusement park ride consists of a cart with some riders (of total mass 200 kg) that is set in motion by a large spring with spring constant 800 N/m. The cart travels along the flat horizontal section of track that is located 17 m above the ground and then down a ramp toward the loop?the?loop which starts at the ground and has an unknown diameter. The entire track is frictionless. Show your work on this one to get full credit!
a. If the spring is initially compressed by 4 m, what is the speed of the cart as it leaves the spring? Is this speed reasonable? (4 pts)
b. What is the speed of the cart at the bottom of the ramp before reaching the loop?the?loop? Is this speed reasonable? (2 pts)
c. What is the maximum height of the loop?the?loop that the cart can do without falling? Is that a reasonable height? (4 pts)
The following applies to questions 7 and 8:
Two carts A and B are identical in all respects. They roll down a hill and collide as shown in the figures at the right.
Figure (i): Cart A starts from rest on a hill at a height h above the ground. It rolls down and collides head-Â??on with cart B which is initially at rest on the ground. The two carts stick together.
Figure (ii): Carts A and B are at rest on opposite hills at heights h/2 above the ground. They roll down, collide head-Â??on with each other on the ground and stick together.
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7. Which of the following statements are true about the two?cart system just before the carts collide in the two cases? Circle all the statements that are true. If none are true, write N. (5 pt)
a. The kinetic energy of the system is zero in case (ii).
b. The kinetic energy of the system is greater in case (i) than
in case (ii).
c. The kinetic energy of the system is the same in both cases.
d. The total momentum of the system is greater in case (ii) than in case (i).
e. The total momentum of the system is the same in both cases.
8. Which of the following statements are true about the two?cart system just after the carts collide in the two cases? Circle all the statements that are true. If none are true, write N. (5 pt)
a. The kinetic energy of the system is greater in case (ii) than in case (i)
b. The kinetic energy of the system is the same in both cases.
c. The momentum of the system is greater in case (ii) than in case (i).
d. The total momentum of the system is non?zero in case (i) while it is zero in case (ii). e. The total momentum of the system is the same in both cases
10. I am riding Zia to UCLA on her new back bike seat, which includes a suspension system of springs to absorb the shock of bumps in the road. When I put the 20?lb Zia into the seat, the springs compress 1 cm.
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(a) When I ride off a sidewalk curb (such as the one in the image) on to the road, the bike bumps to the ground, causing the springs in Zia’s seat to compress further. Estimate this additional compression. Assume the suspension system acts like an ideal spring and the mass of the seat itself is negligible. (5 pts)
(b) Are your values for the spring constant and further compression reasonable? (1 pt)
(Show your work clearly, so we can give you as many partial credit points as possible!)
11. Newton suggested that the force of gravity falls off with distance. The gravitational acceleration at the surface of the earth is about 9.8 m/s2.
a. About how much less is the gravitational force at the top of the lecture hall compared to its value on the floor? Be sure to clearly state your assumptions. (1 pt)
b. About how much less is the gravitational force at the top of Mt. Everest (~9000m above sea level) compared to its value on the
