# exam01_sol_f07 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01 Fall Term 2007 Solutions to Exam 1 Concept Questions: 1. (4 points) (d), same impulse = same momentum. 2. (4 points) (a). 3. (4 points) (e). 4. (4 points) (e). 5. (4 points) (2). Analytic Questions: Problem 2: a) (4 points) x z y ˆ T mg θ b) (6 points) F x = T sin θ f y = 0 F - Z = T cos θ - mg = 0 Using F = m a gives T cos θ = mg T sin θ = m ω 2 ` sin θ Eliminate T to get ω = p g/ ( ` cos θ ) . Exam 1: Solutions 1 October 13, 2007

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c) (10 points) The initial velocities when the string breaks are v x = v z = 0 , and v y = sin θ The time to hit the ground is t = p 2 h/g Thus d = v y t = p 2 h/g `ω sin θ . Problem 3: a) (4 points) T F W mg mg mg θ x d/2 b) (5 points) Calculate the torque about the point where the beam meets the wall. 0 = d T sin θ - 1 2 d mg - x mg - d mg Solve for T T = mg sin θ ± x d + 3 2 ² . c)
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exam01_sol_f07 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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