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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01 Fall Term 2006 Solutions to Exam 2 Concept Questions: 1. (4 points) (d), ω = √ β . 2. (4 points) (d). (Larger wheel has 4 × greater I , requires 4 × torque. As radius is 2 × greater, torque requires 2 × greater F .) 3. (4 points) (d). The impulse is the same, so the heavier cart has half the speed and half the kinetic energy. 4. (4 points) (b). (Just after the impulse F Δ t , case (a) has both masses moving to the right at speed v = F Δ t/ (2 m ) while case (b) has the top mass with speed v = F Δ t/m and the bottom mass at rest. Thus the speed of the CM is the same in both cases, but case (b) has 2 × the kinetic energy.) 5. (4 points) (b). (Position 5 has maximum displacement and zero velocity. Cases (b) and (f) both have v = 0, but (f) corresponds to position 1.) Analytic Questions: Problem 1: a) (4 points) KE i + U i = KE f + U f 0 + 1 2 kx 2 = 1 2 mv 2 ; ⇒ v = x r k m b) (7 points) At the top of the loop you must have...
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