In the figure, a horizontal force ModifyingAbove Upper F With right-arrow Subscr

Question

In the figure, a horizontal force ModifyingAbove Upper F With right-arrow Subscript a of magnitude 21.0 N is applied to a 3.15 kg book as the book slides a distance d = 0.85 m up a frictionless ramp at angle = 30°. (a) During the displacement, what is the net work done on the book by Upper F Overscript right-arrow EndScripts Subscript a, 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 r a of magnitude 21.0 N is applied to a 3.15 kg book as the book slides a distance d = 0.85 m up a frictionless ramp at angle = 30°, (a) During the displacement, what is the net work done on the book by a , 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? (a) Number Units (b) Number Units

Explanation / Answer

a) work done by normal force = 0

work done by gravitational force = wg = -mgdsin30 = -3.15*9.8*0.85*1/2 = -13.12 J

work done by fs = fs*dcos30 = 15.46 J

w tot = 15.46-13.12 = 2.34 J

from work energy theorem

w tot = change in kinetic energy = 1/2mv^2

v = sqrt(2wtot/m) = sqrt(2*2.34/3.15) = 1.22 m/s

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