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Recitation Worksheet K Solutions

# Recitation Worksheet K Solutions - Worksheet K Energy...

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Worksheet K: Energy Diagrams 1. A particle of mass m = 2 kg moves in a region of space with the following potential energy function. a. The force at x = 2 m is _ positive _____ (positive/negative/zero). In the interval x = [4,5] m, the force is __ negative ____ (positive/negative/zero). Explain. The force is minus the slope of the U(x) curve at each point. b. Estimate the magnitude of the force at x = 5 m. The slope of the U(x) curve at x = 5 m is the slope of the tangent line (in blue the figure). That line goes through points (4 m, -10 J) and (5 m, 20 J), so the force is: 20 ( 10) J 30 N 5 4 m U F x − − = − = − = − c. Find the work done by the force when the particle moves from x = 4 m to x = 5 m. ( ) ( ) (5 m) (4 m) 20 ( 10) J 30 J W U U U = −∆ = − = − − − = − d. Is the sign of your answer to part c consistent with your answer to part a? Yes: if you move from 4 m to 5 m (displacement in the +x direction) and the force is in the –x direction, the work should be negative.

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