Question

The drawing shows two boxes resting on frictionless ramps. One box is relatively light and sits on a steep ramp. The other box is heavier and rests on a ramp that is less steep. The boxes are released from rest at A and allowed to slide down the ramps. The two boxes have masses of 9 and 43 kg. If A and B are 4.0 and 0.5 m, respectively, above the ground, determine the speed of (a) the lighter box and (b) the heavier box when each reaches B. (c)What is the ratio of the kinetic energy of the heavier box to that of the lighter box at B?

Answer 1

as vertical distance covered by both the boxes, h = 4 - 0.5 = 3.5 m

also, there exists no any friction loss => change in potential energy = change in kinetic energy

=> mgh = 0.5mv² => v = sqrt(2gh)

a) speed of lighter box, v_L= sqrt(2 x 9.8 x 3.5) = 8.2825 m/s

b) speed of heavier box, v_H = sqrt(2 x 9.8 x 3.5) = 8.2825 m/s

c) ratio of the kinetic energy of the heavier box to that of the lighter box at B = 0.5m_Hv_H²/(0.5m_Lv_L²)

= m_H/m_L = 43/9 = 4.7777778