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Exam2a-sol-Su03

# Exam2a-sol-Su03 - Physics 221 Exam II Summer 2003 The...

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Physics 221. Exam II Summer 2003 The following situation refers to the next two problems: A bobsled slides down a frictionless icy slope and is observed to have a speed of 35 m/s when it crosses the final line (point B). The ground behind the finish line is horizontal and has sand spread on it to slow the bobsled. The coefficient of kinetic friction between the horizontal, rough section and the bobsled is μ k = 0.72. A × h C × B (finish line) × D 51. What was the speed of the bobsled when it was at point A, at height h = 60 m above the finish line? a. v A = 2.1 m/s b. v A = 7.0 m/s c. v A = 9.2 m/s d. v A = 17 m/s e. v A = 31 m/s Use conservation of energy: 2 2 2 1 1 2 2 2 7.0 m/s A B A B mv mgh mv v v gh + = = = 52. The bobsled comes to a stop at point C. Find the distance D between points B and C. a. D = 20 m b. D = 42 m c. D = 61 m d. D = 87 m e. D = 110 m Use the work-kinetic energy theorem. The only force doing work on the bobsled between B and C is friction, so 2 2 1 0 2 87 m 2 B k B k mv mgD v D g µ µ = − = = Page 1 of 13

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Physics 221. Exam II Summer 2003 The following situation refers to the next two problems: A uniform flat plank of mass M = 1000 kg and length L = 10 m floats at rest on a perfectly still lake. A man of mass m = 100 kg stands on one end of the plank. The man begins running to the left. L x x = 0 L 53. When the man reaches the other end of the plank, how far has the plank moved relative to the ground? There are no external forces on the system, so the position of the CM must remain the same before and after the man moves along the plank. Take x = 0 at the left end of the plank before the man starts moving: 2 : CM L M mL Before x m M + = + After, the plank has moved a distance x: 2 CM L M x m x m M + + = + x These two quantities must be the same: 2 2 0.91 m L L M mL M x mx m x L m M + = + + = = + Page 2 of 13
Physics 221. Exam II Summer 2003 54. After he gets to the leftt end of the plank, he turns around and walks back to where he started. His walking speed is less than his running speed. At the end, the position of the plank will be: Using the same argument as before, the position of the plank must be the same. The motion will take longer, but the final result is the same as if the man runs back. Page 3 of 13

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Physics 221. Exam II Summer 2003 The following situation refers to the next two problems: A compressed spring of constant k = 2000 N/m is used to shoot a dart of mass m = 100 g at a wooden block of mass M = 1.0 kg as shown in the figure. When the dart hits the block, it stays pinned on it. Right after the dart hits the block, the speed of the block is measured to be v f = 0.4 m/s.
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Exam2a-sol-Su03 - Physics 221 Exam II Summer 2003 The...

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