In the figure, a horizontal force F a of magnitude 20.0 N is applied to a 2.88 k
ID: 1281023 • Letter: I
Question
In the figure, a horizontal force Fa of magnitude 20.0 N is applied to a 2.88 kg book as the book slides a distance d = 0.35 m up a frictionless ramp at angle theta = 30. (a) During the displacement, what is the net work done on the book by Fa, the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?
In the figure, a horizontal force Fa of magnitude 20.0 N is applied to a 2.88 kg book as the book slides a distance d = 0.35 m up a frictionless ramp at angle theta = 30. (a) During the displacement, what is the net work done on the book by Fa, the gravitational force on the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed at the end of the displacement?Explanation / Answer
WN = N d cos 90 = 0
Wa = Fa * d * cos theta = 20 * 0.35 * cos 30 = 6.06 J
Wmg = m g d cos (90+theta) = 2.88 * 9.81 * 0.35 * cos (90+30) = -4.94 J
To find the final speed, we can use the work to find the change in kinetic energy
Wnet = Wa + Wmg +WN = 1.12 J
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Wnet = delta KE = 1/2 mvf2 - 1/2 mvi2
= 1/2 mvf2 - 0
vf = sqrt [2 Wnet / m]
= sqrt [2 * 1.12 / 2.88]
= 0.882 m/s
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