A child applies a force F? parallel to the x-axis to a 8.00-kg sled moving on th

Question

A child applies a force F? parallel to the x-axis to a 8.00-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 figure (Figure 1) . Suppose the sled is initially at rest at x=0. You can ignore friction between the sled and the surface of the pond. Use the work-energy theorem to find the speed of the sled at 1.0m . Use the work-energy theorem to find the speed of the sled at 9.0m .

Explanation / Answer

E=area undr F-x curve... and .5*m*v(x)^2=E upto x

so E upto x= .5*m*v(x)^2

For part A

E=area upto 1 =area of triangel=.5*height*foot=.5*(10/8*1)*1=.=.625 ...

so .5*m*v(1)^2=.5*8*v(1)^2=.625,,,

so v(1)=.395

at 9 m , F = 10 - (10-0)/(12-8) * 1 =10 - 10/4=7.5 N

area of trapezium = .5 * (l1+l2) * h

Energy upto 9 m = Area of the F-x upto 9 m = area upto 8 m+ area from 8 to 9 = .5*8*10 + (10+7.5) / 2 *1=48.75

E=.5*m*v^2

so 48.75=.5*8*v(9)^2

so v(9)=3.5 m/s

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