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solutions2 - PHYSICS 221 EXAM 2 1[17pt A crate is given an...

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PHYSICS 221 EXAM 2 October 26, 2011 1. [17pt] A crate is given an initial speed of 4.00 m/s up the 30.0 o plane shown in the figure. The coefficient of kinetic friction is 0.200. (a) [3pt] Draw and label all force vectors acting on the box when it is sliding up-hill, taking care to show the directions realistically. (b) [7pt] How far will the box slide up the plane, measured along the slope? Balancing forces in the tilted direction gives while Newton’s second law in the tilted direction gives (taking positive upward) Then . A constant acceleration equation gives with m/s, so that m m. Alternatively, you could use the fact that where is the difference between the final gravitational potential energy and the initial kinetic energy, taking the gravitational energy to be zero at the bottom of the hill, and is the work done by friction, with This implies that Then leading to the same result as above.
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2 (b) [7pt] How fast is the box sliding when it returns to its starting point? The acceleration downhill is , since friction acts against gravity. A constant acceleration equation implies that so Alternative approach: The total work done by friction going up and down the board is (the same work up and down) and gravity is a conservative force (zero
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