PHY131 Midterm2 Solution

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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PHY 131 MIDTERM 2 Version A Put FULL NAME, ID#, and EXAM VERSION on the front cover of the BLUE BOOKLET! Do all problems in order , write legibly , and show all work for partial credit ! Note: make sketches where appropriate and show your axis conventions. Do not forget units, number of signifi- cant digits, and check your results for consistency. This exam will last 1.5 hr. Success! v 0 disk! A 1. A dart of mass m = 0.100 kg (considered a point-like particle) hits a uniform thin cardboard target disk close to its lowest edge with horizontal velocity v 0 = 9.00 m/s perpendicular to the plane of the disk . After hitting, the dart sticks to the card- board. The cardboard disk is suspended loosely at point A on its rim, so that is can swing without friction on an axis tangential to the disk in the plane of the disk. The disk has mass M = 0.400 kg, and radius R = 0.400 m. (Solution) a. Show that the moment of inertia of the disk for this rotation axis is I = 5 MR 2 /4. b. Calculate the angular velocity of the disk plus dart just after collision. c. After collision, disk plus dart rotate around A; show that if the center of the disk rises by a vertical distance h , the dart – stuck at the edge – must rise by 2 h . d. Calculate the maximum vertical distance that the center of the disk rises after collision. 2. A failing elevator car, with total weight W = 20 kN, drops down (from rest) on a safety spring 10 m below, with spring constant k = 60 kN/m and assumed massless. All during the ride, the failing brakes exert a con- stant frictional force on the rails equal to 10 kN. (You may take g = 10 m/s 2 to ease calculations) (Solution) a. Calculate the kinetic energy of the car when it hits the spring.

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