please explain how to solve this problem The drawing shows two boxes resting on

Question

please explain how to solve this problem

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 36 kg. If A and B are 4.5 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?

Explanation / Answer

By energy conservation:

we can write the potential energy at A+kinetic energy at A = potential energy at B+kinetic energy at B.

now, K.E.=1/2*m*v^2 and P.E.= mgh.

for lighter block;

9*9.8*(4.5-1.5)=1/2*9*v^2;

v=7.66 m/sec. (answer a.)

for heavier block;

36*9.8*(4.5-1.5)=1/2*36*v^2.

v=7.66 m/sec. (answer b)

the ratio of their kinetic energies;

r=m1/m2;

(since their velocities are same.)

therefore r= 9/36= 0.25 (answer c)

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