A child applies a force F parallel to the x -axis to a 7.00-kg sled moving on th

Question

A child applies a force F  parallel to the x-axis to a 7.00-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.

a)Use the work-energy theorem to find the speed of the sled at 4.0 m

b)Use the work-energy theorem to find the speed of the sled at 11.0 m .

A 6.0-kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 50 N/cm .

a)Use the work-energy theorem to find the maximum compression of the spring.

Express your answer using two significant figures.

"clear answers plz')

Explanation / Answer

work done = area under the F-X curve
a)
work done = area under triangle formed
    = 0.5*4*5
    = 10 J

Now use work-energy theorem
W = 0.5*m*vf^2
10 = 0.5*7*vf^2
vf= 1.69 m/s
Answer: 1.69 m/s

b)
work done = area under triangle from x=0 to 8 and trapezium formed from x=8 to x=11
    = 0.5*8*10 + 0.5*(10+2.5)*3
    = 40 + 18.75
    = 58.75 J

Now use work-energy theorem
W = 0.5*m*vf^2
58.75 = 0.5*7*vf^2
vf= 4.1 m/s
Answer: 4.1 m/s

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