Question

In the figure, a horizontal force ModifyingAbove Upper F With right-arrow Subscript a of magnitude 18.0 N is applied to a 3.16 kg book as the book slides a distance d = 0.91 m up a frictionless ramp at angle θ = 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?

瓦

Answer 1

(a)

Work done by Fa,

Wa = Fa*d*cos $\Theta$

Wa = 18*0.91*cos30 = 14.185 J

Work done by normal force,

Wn = N*d*cos90 = 0

Work done by gravitaional force,

Wg = m*g*d*cos $\Theta$

Wg = 3.16*9.8*0.91*cos(90 + 30) = -14.090 J

(b)

Wnet = 14.185 - 14.090 = 0.095 J

From Work - Energy Theorem,

Wnet = $\Delta$ KE = KEf - KEi

Wnet = (1/2)*m*v^2 - 0

0.095 = (1/2)*3.16*v^2

v = 0.245 m/s