Question

A mass m = 1 kg slides down a θ = 30◦ inclined plane from a height of 5 m. At the bottom of the incline, it collides with another mass M = 3 kg, and the latter is initially at rest as shown in Fig. 3. The surface to the right of the inclined plane on which the 3 kg (green) mass sits is horizontal.

(a) The inclined surface is frictionless. Conserve energy to find the velocity of the 1 kg (red) mass at the bottom of the incline.

(b) The red mass collides with the 3 kg green mass on the horizontal surface past the inclined plane. Treat the collision as elastic and find the velocities of the masses after collision. Hint: To do this you will need to conserve energy and momentum and solve a quadratic equation.

(c) The path beyond the inlined plane, to the right, turns out to be rough and has a friction coefficient μk = 0.4. Calculate how far the green mass travels before coming to rest. Hint: You can do this using kinematics or energy conservation.

(d) Using energy conservation, determine how far back up the incline did the red block (1 kg) get.

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