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Classical Mechanics

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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?

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)-(c) for a reference point (y = 0) at the elevation where the rock is released. (Neglect air resistance.)

52. Imagine that you swing about your head a ball attached to the end of a string. The ball moves at a constant speed in a horizontal circle. (a) Can the string be exactly horizontal? Why? (b) If the mass of the ball is 0.250 kg, the radius of the circle is 1.50 m, and it takes 1.20 s for the ball to make one revolution, what is the ball's tangential speed? (c) What centripetal force are you imparting to the ball via the string?

56. A clock uses a pendulum that is 75 cm long. The clock is accidentally broken, and when it is repaired, the length of the pendulum is shortened by 2.0 mm. Consider the pendulum to be a simple pendulum. (a) Will the repaired clock gain or lose time? (b) By how much will the time indicated by the repaired clock differ from the correct time (taken to be the time determined by the original pendulum in 24 h)? (c) If the pendulum string were metal, would the surrounding temperature make a difference in the timekeeping of the clock? Explain.

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The solution contains 4 pages providing full step-by-step explanations and derivations of the required expressions and numerical results.

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