Worksheet 136 – Conservation of Energy
H011311C
1. A roller coaster car has a mass of 12,000 kg when full of screaming passengers.
(Note: it has the same mass if the passengers are not screaming). The cart crests a tall hill at point A with a speed of 2.5 m/sec. It continues along the path and passes through the points labeled B, C, and D. Assuming that the track is smooth, what is the speed of the car at each of the points?
2. A ball is dropped off a 26 m high bridge. What is the final speed when it strikes the water?
3. A 1600 kg car is coasting at 24 m/sec along a flat road when it begins to move up an icy slope. If the slope is inclined at 8 degrees, what height above the flat road will the car reach? What length along the slope will the car travel?
4. A .06 kg tennis ball is tossed straight up with an initial velocity of 14 m/sec. What maximum height does it reach when the tennis ball stops?
5. A pole vaulter runs with an initial speed of 8.5 m/sec. She clears the bar with a final speed of 1.2 m/sec. Assuming minimal energy is lost to friction, what is the height of the bar. Assume her mass is 54 kg.
6. An 800 N/m spring is fixed to a wall so that it can be compressed in a horizontal direction.. The spring is compressed a distance of .2 m. A 12 kg mass is placed at the end of the spring. If it starts from rest, what is the speed of the mass when the spring is completely outstretched?
7. Now, assume that the mass in question 6 slides across a frictionless floor and slides up a frictionless incline. If the incline is raised to 15 degrees, what length along the incline will the object travel before it stops?
8. A 7500 kg truck is traveling along the highway at 30 m/sec when the brakes give out and the truck strikes a rubber safety bumper. (They have these at toll booths and sometimes at exit ramps). Assume the bumper obeys Hook’s Law, and that the spring constant of the bumper is 5.5 x 105 N/m. What is the depression of the bumper when the truck comes to a stop?
9. An elevator shaft employs a large spring as a safety mechanism at the bottom of the shaft. Assume the safety spring has a spring constant of 6.4 x 105 N/m. The elevator has a mass of 4,800 kg and falls from a height of 25 meters when it reaches the spring.
A. What is the speed of the elevator when it reaches the springs?
B. When the elevator stops oscillating on the spring and everything comes to a rest, what is the compression of the spring?
10. A spring is placed into a recessed hole in the floor. When not compressed or stretched the top of the spring is level with the floor. A 5 kg bowling bowl is then placed on top of the spring. This causes the spring to compress to a distance of .1 m below the floor. The spring is then manually compressed to a total distance of .5 m below the floor. The spring is then released, thrusting the ball into the air. What is the maximum height of the ballabove the floor?