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Unformatted text preview: yindeemark (rry82) Homework 12 chelikowsky (59005) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Assume: A bullet of mass m and cube of mass M undergo an inelastic collision, where m M . Note: The moment of inertia of this cube (with edges of length 2 a and mass M ) about an axis along one of its edges is 8 M a 2 3 . A solid cube is resting on a horizontal sur- face. The cube is constrained to rotate about an axis at its bottom right edge (due to a small obstacle on the table). A bullet with speed v min is shot at the left-hand face at a height of 4 3 a . The bullet gets embedded in the cube. 2 a M mvectorv min 4 3 a M g Find the minimum value of v min required to tip the cube so that it falls its right-hand face. 1. v min = m M radicalbigg 5 g a parenleftBig 2 1 parenrightBig 2. v min = M m radicalbigg 3 g a parenleftBig 2 1 parenrightBig correct 3. v min = m M radicalbigg 2 g a parenleftBig 2 1 parenrightBig 4. v min = m M radicalbigg 3 g a parenleftBig 5 1 parenrightBig 5. v min = m M radicalbigg 3 g a parenleftBig 3 1 parenrightBig Explanation: Basic Concepts: summationdisplay vector L = const U + K = 0 For the cube to tip over the center of mass (CM) must rise so that it is over the axis of rotation AB . To do this the CM must be raised a distance of a parenleftBig 2 1 parenrightBig . From conservation of energy M g a parenleftBig 2 1 parenrightBig = 1 2 I cube 2 . (1) From conservation of angular momentum 4 a 3 mv = parenleftbigg 8 M a 2 3 parenrightbigg = parenleftBig mv 2 M a parenrightBig . (2) Thus, substituting Eq. 2 into 1, we have 1 2 parenleftbigg 8 M a 2 3 parenrightbiggparenleftbigg m 2 v 2 4 M 2 a 2 parenrightbigg = M g a parenleftBig 2 1 parenrightBig Solving for v yields v min = M m radicalbigg 3 g a parenleftBig 2 1 parenrightBig . 002 10.0 points If you walk along the top of a fence, why does holding your arms out help you to balance? 1. Your momentum is decreased. 2. Your rotational inertia is decreased. 3. Your rotational inertia is increased. cor- rect 4. Your momentum is increased. Explanation: Your rotational inertia increases when your arms are outstretched, which increases the resistance to a change in your rotational state. 003 10.0 points The angle of the inclination is 34 . 9 , the outer part of the large pulley has a radius of 3 r and the inner part of the large pulley has a radius of r . yindeemark (rry82) Homework 12 chelikowsky (59005) 2 3 r r /2 r m T Find the mass m needed to balance the 820 kg truck on the incline. The acceleration of gravity is 9 . 8 m / s 2 . Assume all pulleys are frictionless and massless and the cords are massless....
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