mid2v1sol - Ph 111.01 October 27, 2008 SEAT NUMBER NAME...

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Ph 111.01 October 27, 2008 SEAT NUMBER NAME Midterm II Solutions Please answer all of the problems, showing your work and explaining your reasoning. You may refer to your formula sheets, two pages (both sides). Please express all numerical answers to at least three significant figures, and give the corresponding units (m, N, s, rad/s 2 , etc). Please take the acceleration of gravity to be exactly g = 9.8 m/s 2 . Midterm 2, Ph 111.01 Fall 2008 0 2 4 6 8 10 12 0 4 8 12 16 20 24 28 32 36 40 44 48 score (out of 50) average = 23.7/50, 117 people B A C
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N mg Problem 1. A hockey puck of mass m = 2 kg is attached by a string (string tension = T ) to a pivot point in the center of a table, as shown from above in the diagram. The hockey puck moves in a circle of radius R = 2 m, with constant speed v = 4 m/s. y x R v m m y x T (a ) Make a free-body diagram for the hockey puck in the space provided to the right of the diagram. Show all the forces acting in the horizontal direction on the hockey puck, but only forces. Each force should be labeled appropriately. Plot only horizontal forces. (Not or .) Just one force, the tension, towards the center of the circle. (b) What is the angular velocity ω of the hockey puck? 4 m/s 2 rad/s v == = 2 m r = 2 rad/s (c) What is the acceleration (direction and magnitude) of the hockey puck? ? This is the centripetal acceleration. The direction is towards the center of the circle, which would be the -y direction in the diagram. The magnitude is given by () 2 2 2 cen 4 m/s 8 m/s v a = R acceleration: direction (+x, -x, +y, -y) =-y magnitude =8m/s 2 (d) What is the tension T in the string? From Newton's second law in the y direction 2 "" 2 kg 8 m/s 16 N Fm a Tm a = = T = 16 N
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Problem 2. A crate with a mass of m = 10 kg is sliding at a constant speed v 1
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mid2v1sol - Ph 111.01 October 27, 2008 SEAT NUMBER NAME...

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