6. A box of textbooks of mass 25 kg rests on a loading ramp that makes an angle

Question

6. A box of textbooks of mass 25 kg rests on a loading ramp that makes an angle = 16° with the horizontal. The coefficient of kinetic friction is 0.2. When the box is released, it starts sliding down the incline. The length of the ramp is 5 m. (a) Find the normal force on the box (b) Find the frictional force (c) Find the gravitational force (d) Find the work of gravitational force (e) Find the work of normal force (?) Find the work of frictional force (g) Find the total work (h) Find the velocity of the box at the end of ramp, using work-energy theorem.

Explanation / Answer

When the box is kept on an incline, the weight of the box is divided in two components.
One component mgcos16 is balanced out by the normal reaction and mgsin16 is what makes the box slide down.

Normal force = mgcos16 = 25*10*0.961 = 240.31 N
Frictional force = coeff of friction * normal force = 0.2 * 240.31 = 48.06 N
Gravitational force = mgsin16 = 25*10*0.27 = 68.90 N
Work done by gravitational force = force * displacement = 68.90 *length of ramp = 68.90 * 5 = 344.54 J
Work done by normal force = normal * displacement in the vertical direction = 240.31 * 0 = 0 J

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