A child applies a force F ? parallel to the x -axis to a 10.0- k g sled moving o

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.

A child applies a force F parallel to the x-axis to a 1.-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=. 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 5.m. Correct Significant Figures Feedback: Your answer 1.78 m/s was either rounded differently or used a different number of significant figures than required for this part. Use the work-energy theorem to find the speed of the sled at 12.m.

Explanation / Answer

Slope of graph betwwen x = 0 to x= 8 is 10/8 i.e. 5/4

so F = 5*x/4

1) Work done = KE

integral (Fdx) = 0.5*m*v^2

integral(5xdx/4) = 0.5*10*v^2

5*x^2/8 = 5*v^2

Put x=5

125/8 = 5*v^2

v = sqrt(25/8) = 1.7677 m/s

2) Work done = Area ounder curve = 0.5*m*v^2

0.5*8*10 + 0.5*(12-8)*10 = 0.5*10*v^2

80 + 40 = 10*v^2

12 = v^2

v = sqrt(12) = 3.464 m/s

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