One box is relatively light and sits on a steep ramp. Theother box is heavier an

Question

One box is relatively light and sits on a steep ramp. Theother box is heavier and rests on a ramp that is less steep. Theboxes are released from rest at A and allowed to slide down theramps. The two boxes have masses of 15and 33 kg. If A and B arehA = 4.6 andhB = 1.3 m,respectively, above the ground, determine the speed of (a) thelighter box and (b) the heavier box when each reaches B. (c) Whatis the ratio of the kinetic energy of the heavier box to that ofthe lighter box at B? One box is relatively light and sits on a steep ramp. Theother box is heavier and rests on a ramp that is less steep. Theboxes are released from rest at A and allowed to slide down theramps. The two boxes have masses of 15and 33 kg. If A and B arehA = 4.6 andhB = 1.3 m,respectively, above the ground, determine the speed of (a) thelighter box and (b) the heavier box when each reaches B. (c) Whatis the ratio of the kinetic energy of the heavier box to that ofthe lighter box at B?

Explanation / Answer

(a) if the surfaces are frictionless (which I guess weassume they are) then the speeds of both boxes are the same. Thisis because... .     final kinetic energy = decreasein potential energy .    (1/2) m v2   = m gh .      v = 2gh            notice that mass disappears from the equation. So... .     v = 2*9.80*(4.6-1.3)   =    8.042 m/s    is the speed of both boxes. . (c)   the kinetic energies are proportional to themasses, so the ratio of the kinetic energies is the same as theratio of the masses:   33 / 15  =  2.20 . (c)   the kinetic energies are proportional to themasses, so the ratio of the kinetic energies is the same as theratio of the masses:   33 / 15  =  2.20

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