Instructions: Read the following paragraph carefully. Then use what you know about momentum, work, and energy to answer the following questions. Be sure to show your work.

You are a traffic accident investigator. You have arrived at the scene of an accident. Two cars of equal mass (1,000 kg each) were involved in a rear-end accident at a stop sign. Here is what you know:

Car 1 approached the intersection from the top of a 25-meter hill.
Car 2 was on a flat stretch of road directly in front of Car 1.
At the bottom of the hill, Car 1 was going 20 m/s; Car 2 was going 30 m/s before it stopped at the stop sign.
There were no skid marks left by Car 2. The collision occurred at the stop sign, where Car 2 had stopped.
After the collision, both cars were moving together in the same direction at 10 m/s before slowly rolling to a stop.
You must now push Car 2, using 800 N of force, 10 meters off to the side of the road so no one else gets hurt.
1. What was the potential energy of Car 1 at the top of the hill?

2. What was the kinetic energy of each car before braking?

3. A. How much energy did Car 1 lose from the top to the bottom of the hill?

B. Where do you suppose that energy went?

4. How much work was done to bring Car 2 to a stop?

5. If Car 2 came to a stop in 15 seconds, how much power (in watts) did it take to stop Car 2 at the stop sign by applying force to the brakes?

6. What is the final combined momentum of the cars right after the accident?

7. Assuming that there are no other nonconservative forces involved, what impulse was given to each car during the collision?
A. Car 1

B. Car 2

8. How much energy did Car 1 lose in the collision?

9. How much energy did Car 2 gain in the collision?

10. Which of the two laws covered in this unit - Law of Conservation of Momentum or Law of Conservation of Energy - is obeyed in this problem? Explain your reasoning.

11. How much work did it take to move Car 2 off to the side of the road?

12. If it took you 40 seconds to move Car 2 off the road, how much power did you expend?

13. Which simple machine does a car have that helped you move Car 2? Explain.

To answer these questions, we will need to use the concepts of momentum, work, and energy. Let's go through each question step by step and explain how to find the answer.

1. To find the potential energy of Car 1 at the top of the hill, we can use the formula: Potential Energy = mass * gravity * height. The mass of Car 1 is 1,000 kg, and the height of the hill is 25 meters. The value of gravity is approximately 9.8 m/s^2. So, Potential Energy = 1,000 kg * 9.8 m/s^2 * 25 meters.

2. To find the kinetic energy of each car before braking, we can use the formula: Kinetic Energy = (1/2) * mass * velocity^2. The mass of each car is 1,000 kg. Car 1 had a velocity of 20 m/s, and Car 2 had a velocity of 30 m/s.

3. A. To find the energy lost by Car 1 from the top to the bottom of the hill, we need to subtract its final kinetic energy from its initial potential energy.
B. The energy lost is converted into other forms, such as heat, sound, and deformation of the cars.

4. To find the work done to bring Car 2 to a stop, we can use the formula: Work = force * distance. The force applied is 800 N, and the distance over which it is applied is 10 meters.

5. To find the power used to stop Car 2 at the stop sign, we can use the formula: Power = Work / time. The time taken is 15 seconds.

6. To find the final combined momentum of the cars after the accident, we can add the individual momenta of the cars. Momentum = mass * velocity.

7. Assuming no other nonconservative forces, the impulse given to each car during the collision can be found using the formula: Impulse = change in momentum.

8. To find the energy lost by Car 1 in the collision, we need to subtract its final kinetic energy from its initial kinetic energy.

9. To find the energy gained by Car 2 in the collision, we need to subtract its initial kinetic energy from its final kinetic energy.

10. We need to determine which law, the Law of Conservation of Momentum or the Law of Conservation of Energy, is obeyed in this problem by examining whether the total momentum and total energy of the system are conserved or not.

11. To find the work required to move Car 2 off the side of the road, we can use the formula: Work = force * distance. The force applied is 800 N, and the distance is 10 meters.

12. To find the power expended to move Car 2 off the road in 40 seconds, we can use the formula: Power = Work / time. The time taken is 40 seconds.

13. We need to identify the simple machine in the car that helped move Car 2. Simple machines in cars could include wheels and axles, as well as the use of ramps or inclined surfaces for lifting or moving.

Now that we have understood how to approach each question, you can try to solve them using the given information and formulas.