You have been assigned to design a package moving system as shown in the figure.

Question

You have been assigned to design a package moving system as shown in the figure. Boxes start at the top of the ramp with some initial velocity. They slide down a nearly frictionless part of the ramp and then are stopped due to friction on the horizontal part of the ramp. The ramp has a height of h = 1.8 m, the initial velocity of the boxes is vi = 1.8 m/s, and the distance the box should travel before stopping is xf = 5.6 m. This is the distance from where the friction starts, (x=0 in the figure) on the horizontal part of the ramp.

What should be the coefficient of friction, ?k in this case? Give your answer to 3 significant figures (it has no units).

Explanation / Answer

from the law of conservation of eenrgy

PE + KE = net work done

mgh + 0.5 mv^2 = u mg xf

cancelling m on noth sides

9.81 * 1.8 + 0.5*1.8^2 = u * 9.81 * 5.6

u = 0.35 is the kinetic friction

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