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section%201%20soln

section%201%20soln - m a = m b ~ v = ~ v f a ~ v f b and v...

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Problem 1 Let T be the tension in the rope between the drum and the pulley, R be the radius of both the drum and the pulley, and M = 2 kg be the mass of both the drum and the pulley. Σ τ drum = TR = I drum α drum = MR 2 α drum Σ τ pulley = TR - FR = I pulley α pulley = 1 2 MR 2 α pulley F pulley = T + F - Mg = ma pulley = 0 α drum = - α pulley TR = MR 2 α and FR - TR = 1 2 MR 2 α TR = 2 FR - 2 TR 3 T = 2 F T = 2 3 F T + F - mg = 0 2 3 F + F = 5 3 F = mg F = 3 5 mg F = 3 5 ( 2 kg )( 9.8 m s 2 ) = 11.76 N 1

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Problem 5 Conservation of momentum m a ~ v 0 = m a ~ v f a + m b ~ v f b This is an elastic collision, so we can conserve kinetic energy 1 2 m a v 2 0 = 1 2 m a v 2 f a + 1 2 m b v 2 f b
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Unformatted text preview: m a = m b ~ v = ~ v f a + ~ v f b and v 2 = v 2 f a + v 2 f b ~ v Â· ~ v = ( ~ v f a + ~ v f b ) Â· ( ~ v f a + ~ v f b ) â‡’ v 2 = v 2 f a + v 2 f b + 2 ~ v f a Â· ~ v f b â‡’ v 2 f a + v 2 f b = v 2 f a + v 2 f b + 2 ~ v f a Â· ~ v f b â‡’ ~ v f a Â· ~ v f b = Since ~ v f a Â· ~ v f b = 0, the angle between ~ v f a and ~ v f b is 90 â—¦ Â± 1...
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section%201%20soln - m a = m b ~ v = ~ v f a ~ v f b and v...

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