Please Provide All solutions for the answer to these problems. I have the answer I am looking at how you came to this answer.

1. A car drives 5.0 km north, then 7.3 km east, then 6.7 km northeast, all at a constant velocity. If the car had to perform 2.6 × 106 J of work during this trip, what was the magnitude of the average frictional force on the car?

2. A spring with a spring constant of 10 N/m is stretched from equilibrium to 2.9 m. How much work is done in the process?

3. 300 J of work are required to fully drive a stake into the ground. If the average resistive force on the stake by the ground is 355 N, how long is the stake?

4. Three cars (car L, car M, and car N) are moving with the same velocity, and slam on the brakes. The most massive car is car L, and the least massive is car N. Assuming all three cars have identical tires, for which car is the amount of work done by friction in stopping it the highest?

5. Sue and Betti both ski straight down a hill, both starting from rest. Sue weighs more than Betti. Neglecting friction and wind resistance, which skier will be moving the fastest at the bottom of the hill?

6. 188 J of work are needed to stretch a spring from 1.4 m to 2.9 m from equilibrium. What is the value of the spring constant?

7. A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 325 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

8. How much work must be done by frictional forces in slowing a 1000.0 kg car from 27.8 m/s to rest?

9. A 31 g bullet pierces a sand bag 24 cm thick. If the initial bullet velocity was 31 m/s and it emerged from the sandbag with 13 m/s, what is the magnitude of the friction force (assuming it to be constant) the bullet experienced while it traveled through the bag?

10. 4.00 × 105 J of work are done on a 1033 kg car while it accelerates from 10.0 m/s to some final velocity. Find this final velocity.

11. A child pulls on a wagon with a force of 75 N. If the wagon moves a total of 42 m in 3.2 min, what is the average power generated by the child, in watts?

12. A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time (neglect friction and assume the spring obeys Hooke’s law)?

13. Three cars with identical engines and tires start from rest, and accelerate at their maximum rate. Car X is the most massive, and car Z is the least massive. Which car needs to travel the furthest distance before reaching a speed of 60 mi/h?

14. A 5.7 m massless rod is loosely pinned to a frictionless pivot at 0. A 4.0 kg ball is attached to the other end of the rod. The ball is held at A, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely in a vertical circle between A and B. In the figure, the ball passes through C, where the rod makes an angle of 30° below the horizontal. The speed of the ball as it passes through C is closest to:

15. A spiral spring is compressed so as to add U units of potential energy to it.

When this spring is instead stretched two-thirds of the distance it was compressed, its remaining potential energy in the same units will be.

16. A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below?

17. Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. The maximum height of Joe’s ball will be

18. A tennis ball bounces on the floor three times. If each time it loses 23% of its energy due to heating, how high does it bounce after the third time, provided we released it 1.1 m from the floor?

19. In the absence of friction, how much work would a child do while pulling a 12 kg wagon a distance of 4.2 m with a 22 N force?

20. An engine is being used to raise a 89 kg crate vertically upward. If the power output of the engine is 1620 W, how long does it take the engine to lift the crate a vertical distance of 18.7 m? Friction in the system is negligible.

21. You carry a 7.0 kg bag of groceries 1.2 m above the ground at constant velocity across a 6.9 m room. How much work do you do on the bag in the process?

22. A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 8.8 m above the ground. What is the mass of the box?

23. Two balls having different masses reach the same height when shot into the air from the ground.

If there is no air drag, which of the following statements must be true? (More than one statement may be true.)

24. A 1000.0 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 17.0 m/s. How far does it travel while slowing down?

25. A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 meters. The sand is initially at rest and is discharged at the top of the sand mover with speed 5 m/s into a loading chute. At what minimum rate must power be supplied to this machine?

26. A brick is dropped from the top of a building through the air (friction is present) to the ground below.

How does the brick’s kinetic energy (K) just before striking the ground compare with the gravitational potential energy (Ugrav) at the top of the building? Set y=0at the ground level.

27. A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. Assuming the elevation loss of the three rocks is the same (the base of the cliff is flat), which rock hits the ground with the highest speed?

28. You slam on the brakes of your car in a panic and skid a distance d on a straight and level road.

If you had been traveling twice as fast, what distance would the car have skidded under the same conditions?

29. Spring #1 has a force constant of k, and spring #2 has a force constant of 2k. Both springs are attached to the ceiling, identical weights are hooked to their ends, and the weights are allowed to stretch the springs.

The ratio of the energy stored by spring #1 to that stored by spring #2 is

30. Consider two frictionless inclined planes with the same vertical height. Plane 1 makes an angle of 25.0∘ with the horizontal, and plane 2 makes an angle of 60.0∘ with the horizontal. Mass m1 is placed at the top of plane 1, and mass m2 is placed at the top of plane 2. Both masses are released at the same time.

At the bottom, which mass is going faster?

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