A child applies a force \\(\\vec F\\) parallel to the \\(x\\)-axis to a 6.00-\\(

Question

A child applies a force  (ec F) parallel to the (x)-axis to a 6.00-( m 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.

Exercise 6.37 Part A A child applies a force vec Fl) parallel to the xl)-axis to a 6.00- kgl) sled moving on the frozen surface of a small pond. As the child controls the speed of the sled, the Vxl)-component of the force she applies varies with the Vx-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 8.0 frm m) Ovi)= 3.65 nrm misi) Submit My Answers Give Up Correct Part B Use the work-energy theorem to find the speed of the sled at 12.0 rm m) (rm m/s) Submit My Answers Give Up de Feedbac Continue Figure 1 c 1 F (N) 0 r (m) 0 4

Explanation / Answer

Part A]

Work Done = area under the curve for the graph

W = (1/2) x base x height = (1/2)(8)(10) = 40 J

by work-energy theorem, this must be equal to the kinetic energy

K.E = (1/2)mv2 = 40

=> (1/2)(6)v2 = 40

=> v = 3.6515 m/s

this is the velocity at x = 8 m

Part B] W = 40 + (1/2)(12 - 8)(10) = 60 J

so, by work energy theorem, 60 = (1/2)mv2

=> v = 4.472 m/s. This is the speed at x = 12m.

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