A child applies a force F parallel to the x-axis to a 10.0-kg sled moving on the

Question

A child applies a force F 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 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. Part A Use the work-energy theorem to find the speed of the sled at 1.0 m .

Part B Use the work-energy theorem to find the speed of the sled at 10.0 m .

Explanation / Answer

According to work energy theorem, work done is equal to change in energy

       m g d = ( 1/ 2 ) m v 2

        v = sqrt ( 2 g d )

A) at d = 1 m

      v = sqrt ( 2 (9.8 m/s2 ) ( 1 m ) )

          = 4.42 m/s

B)

   v = sqrt ( 2 ( 9.8 m/s2 ) ( 10 m ) )

       =14 m/s

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