ReviewAnswers - Phys 2101 Review problems In the figure...

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Phys 2101 Review problems
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In the figure below, block 1 of mass m 1 slides from rest along a frictionless ramp from height h = 3.00 m and then collides with stationary block 2, which has mass m 2 = 2m 1 . After the collision, block 2 slides into a region where the coefficient of kinetic friction k is μ k =0.6 and comes to a stop in distance d within that region. (a) What is the distance d if the collision is elastic? Ans:(4/9)h/ μ k =2.22m (b) What is it if the collision is completely inelastic? Ans: (1/9) h/ μ k =0.56m (c) What is the final velocity of block 1 if d=1m? Ans: (2gh) 1/2 - (8g μ k d) 1/2 =0.81 m/s (leftward) (d) Are the answers the same if block 1 is a rolling cylinder with the same mass? Ans: yes, if the ramp if frictionless (cylinder will slide, not roll); if cylinder rolls, the answers are different due to rotational (rolling) kinetic energy.
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A block of mass m falls from rest from a distance h above a mass M which is at rest at the top of a spring of length L when relaxed. When the mass m falls, the two masses stick together, compress the spring, then the spring pushes back and the two masses go up. (a) When is the potential energy stored in the spring maximum and what is it? Ans: when the spring is maximally compressed spring potential energy will be U s =(1/2)kx m 2 where x m is the solution of a quadratic equation, x m = [(m+M)g ± mg{1- 2kh/[g(m+M)]} 1/2 ]/k representing maximum compression of the relaxed spring which is by Mg/k larger than the drawn position. (b) How far up will the two masses go? Ans: H=2(x m -x e ) where x e =(m+M)g/k is the equilibrium position and x m -x e is the amplitude of the oscillations.
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Cont (c) What is the maximum velocity of mass m while moving alone? Ans: (2gh) 1/2 , just before it collides with M (d) What is the maximum velocity of the two masses stuck together? Ans: v m =(x m -x e ) ω where ω =(k/(m+M)) 1/2
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The 0.5 kg iron ball shown is being swung in a vertical circle at the end of a 0.7-m long string.
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