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.

1) Use the work-energy theorem to find the speed of the sled at 8.0 m .

2) Use the work-energy theorem to find the speed of the sled at 12.0 m

Explanation / Answer

1) According to work-energy theorem,

Workdone = change in kinetic energy

0.5*base*height = 0.5*m*(vf^2 - vi^2)

0.5*8*10 = 0.5*7*(vf^2 - 0)

40 = 3.5*vf^2

==> vf = sqrt(40/3.5)

= 3.38 m/s

2) According to work-energy theorem,

Workdone = change in kinetic energy

0.5*base*height = 0.5*m*(vf^2 - vi^2)

0.5*12*10 = 0.5*7*(vf^2 - 0)

60 = 3.5*vf^2

==> vf = sqrt(60/3.5)

= 4.14 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.