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# Several mechanics problems.

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38. In an emergency stop to avoid an accident, a shoulder-strap seat belt holds a 60-kg passenger firmly in place. If the car were initially traveling at 90 km/h and came to a stop in 5.5 s along a straight, level road, what was the average force applied to the passenger by the seatbelt?

50. Jane and John, with masses of 50 kg and 60 kg, respectively, stand on a frictionless surface 10 m apart. John pulls on a rope that connects him to Jane, giving Jane an acceleration of 0.92 m/s[squared] toward him.

(A) What is John's acceleration?
(B) If the pulling force is applied constantly, where will Jane and John meet?

54. A 75.0-kg person is standing on a scale in an elevator. What is the reading of the scale in newtons if the elevator is

(a) at rest?
(b) moving up at a constant velocity 2.00m/s
(C) accelerating up at 2.00m/s[squared]

88. A packing crate is placed on a 20-degree inclined plane. If the coefficient of static friction between the crate and the plane is 0.65, will the crate slide down the plane? Justify your answer.

42. A 1200-kg automobile travels at a speed of 90 km/hr.

(a) What is its kinetic energy?
(b) What is the net work that would be required to bring it to a stop?

44. A 3.0-g bullet traveling at 350 m/s hits a tree and slows down uniformly to a stop while penetrating a distance of 12 cm into the tree's trunk. What was the force exerted on the bullet in bringing it to rest?

66. A person standing on a bridge at a height of 115 m above a river drops a 0.250 kg- rock.
(A) What is the rock's mechanical energy at the time of release relative to the surface of the river?
(B) What are the rock's kinetic, potential, and mechanical energies after it has fallen 75.0 m?
(C) Just before the rock hits the water, what are its speed and total mechanical energy?
(D) Answer parts (A) to (C) for a reference point (y = 0) at the elevation where the rock is released. (Neglect air resistance.)

76. A 1.5-kg box that is sliding on a frictionless surface with a speed of 12 m/s approaches a horizontal spring. The spring has a spring constant of 2000 N/m.

(A) How far will the spring be compressed in stopping the box?
(B) How far will the spring be compressed when the box's speed is reduced to half of its initial speed?

88. A 60-kg woman runs up a staircase 15 m high (vertically) in 20 s.

(A) How much power does she expend?
(B) What is her horsepower rating?

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the solution is 9 pages long including full explanations, derivations, diagrams and equations dealing with a range of common topics in Newtonian mechanics.

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