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 11 and 31 kg. If A and B are 5.0 and 1.5 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

Answer

given,

two box of masses = M_a = 11 kg

                                  M_b = 31 Kg

If A and B are 5.0 and 1.5 m, respectively, above the ground.

h = 5 - 1.5 = 3.5 m

a) , b) using energy conservation

$mgh = \dfrac{1}{2}mv^2$

$v = \sqrt{2gh}$

velocity of the lighter  and heavier box

$v = \sqrt{2\times 9.8 \times 3.5}$

v = 8.29 m/s

c ) ratio of kinetic energy

  $\dfrac{KE_{heavy}}{KE_{light}}=\dfrac{ \dfrac{1}{2}Mv_h^2}{ \dfrac{1}{2}mv_l^2}$  

$\dfrac{KE_{heavy}}{KE_{light}}=\dfrac{ M}{ m}$

$\dfrac{KE_{heavy}}{KE_{light}}=\dfrac{31}{11}$

ratio = 2.82