# 2b the same box is pushed by a 20 nm spring as it

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2b. The same box is pushed by a 2.0 N/m spring as it relaxes, from x=-5.0cm to x=0.0 cm. What is the work done by the spring? W = - 1 2 (2 . 0)((0) 2 - ( - 5 . 0) 2 ) J = +25 J You can ’t fail to notice that in both examples the work for the round trip vanishes.

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Phys 2A - Mechanics 3a. The same box is pushed on a rough surface with coefficient of kinetic friction 0.7 from the origin to the point x=1.0m. Determine the work done by the force of friction. The examples above must seem vaguely familiar, they look a lot like the computation of potential. Here is something new: W = Z x f x i F friction ,x dx = Z x f x i ( - μ k mg ) dx = - μ k mg ( x f - x i ) W = - (0 . 7)(20)(9 . 8)(1 . 0 - 0) J = - 140 J 3b. The same box is pushed on a rough surface with coefficient of kinetic friction 0.7 from the point x=1.0m to the origin. Determine the work done by the force of friction. W = Z x f x i F friction ,x dx = Z x f x i (+ μ k mg ) dx = + μ k mg ( x f - x i ) W = +(0 . 7)(20)(9 . 8)(0 - 1 . 0) J = - 140 J Wow! The work done on the round trip does not vanish! Motion to the right Force points left: negative Motion to the left Force points right: positive
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