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 10 and 37 kg. If A and B are hA = 4.4 and hB = 1.7 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

To find the speed of the lighter and heavier box when they reach point B, we can use the principle of conservation of energy. The ratio of their kinetic energies at B can also be determined.

Step-by-step explanation:

To determine the speed of the lighter box when it reaches point B, we can use the principle of conservation of energy. The potential energy of the box at A is converted into kinetic energy at B. The potential energy at A is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. The kinetic energy at B is given by KE = (1/2)mv^2, where v is the speed. By equating the two expressions and solving for v, we can find the speed of the lighter box.

For the heavier box, we can use the same principle of conservation of energy. Since both boxes start at rest, they have the same initial potential energy at A. Therefore, the heavier box will have a larger final kinetic energy at B, and hence a greater speed. We can use the same formula as before to calculate the speed of the heavier box.

To find the ratio of the kinetic energies of the two boxes at B, we can simply divide the kinetic energy of the heavier box by the kinetic energy of the lighter box.