Final-solutions 1

# Final-solutions 1 - PHYSICS 221 FINAL EXAM Section 1...

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PHYSICS 221 FINAL EXAM Section 1, December 2010 SOLUTIONS Problem 1: [12pt] A football player kicks a ball with a speed of 22.0 m/s at an angle of 49.0 o above the horizontal, a distance of 39.0 m from the goal post. (a) [6pt] What is the height of the ball above the ground when it reaches the goal post? The horizontal and vertical position are given by with m/s, m/s. Then 39 m/(14.4 m/s) 2.71 s, and (b) [6pt] What is the ball’s vertical velocity when it reaches the goal post? Give a positive velocity upward, negative downward.

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2 Problem 2: [12pt] A uniform ladder has a length of m and it leans against a frictionless wall at an angle of , as shown. The ladder weighs 34.0 lb, and a 90.0 lb boy climbs a distance m up the ladder. (a) [6pt] Find the magnitude of the frictional force in pounds. (There is no need to convert units.) Let and denote the weight of the ladder and boy. Balancing torques about the bottom of the ladder gives Balancing forces in the horizontal direction gives Therefore, (b) [6pt] If the floor is slippery and has coefficient of friction with the ladder, what is the greatest distance the boy can climb before the ladder slips? The same equations apply as in part (a), together with and the vertical equilibrium condition Then (0.250) (124 lb) = 31.0 lb. Now is unknown, and satisfies
3 Problem 3: [12pt] A ball of mass kg is dropped from a height m above a large spring with spring constant 600 N/m. (a) [6pt] What is the total work done on the ball during the spring’s compression , from the time it contacts the spring to the time it momentarily comes to rest? Include the correct sign. The work done on the ball is its change in kinetic energy, By energy conservation, the kinetic energy of the ball at the top of the spring is Therefore, (b) [6pt] Find the maximum compression distance of the spring before it rebounds.

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