A child applies a force F %u20D7 parallel to the x -axis to a 10.0- k g sled mov
ID: 2119965 • Letter: A
Question
A child applies a force F%u20D7 parallel to the x-axis to a 10.0-kg sled moving on the frozen surface of a small pond. As the child controls the speed of the sled, the x-component of the force she applies varies with the x-coordinate of the sled as shown in figure1, Suppose the sled is initially at rest at
x=0. You can ignore friction between the sled and the surface of the pond.
A)Use the work-energy theorem to find the speed of the sled at 5.0m .
B)Use the work-energy theorem to find the speed of the sled at 11.0m .
Explanation / Answer
a)
by the given graph,
work done from 0 to 5m = area under curve = 0.5*5*(25/4) = 15.625 J
word done = KE = 1/2mV^2
15.625=0.5*10*V^2
V = sqrt(15.625/(0.5*10)) = 1.78 m/s
b)
work done from 0 to 11m = area under curve = 0.5*8*10+0.5*4*10-0.5*1*2.5 = 58.75 J
word done = KE = 1/2mV^2
58.75=0.5*10*V^2
V = sqrt(58.75/(0.5*10)) = 3.43 m/s
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