Question

A 1kg ring with a radius of 10 cm rolls down a board inclined at 30 degrees from a height of 4 meter. At the bottom of the inclined, n a frictionless table fits a 3-kg block. After coming off of the incline, the ring slides (without rolling) until colliding and coupling with the block. The ring-block system then continues to move and flies off the edge of the 1.5 meter high table. What is the velocity of the ring-block system after the collision?

Answer 1

The idea behind the problem is to calculate the linear velocity of the ring before collision, and then apply the principle of conservation of linear momentum to find the velocity of the ring-block system.

At first, it seems that we have to calculate the angular velocity of the ring, etc. However, note that after the ring is off the slope, it doesn't roll, and its kinetic energy is conserved because no external force is acting on it. Therefore, its kinetic energy just before hitting the block is equal to its change in potential energy.

This is equal to the pre-collision kinetic energy of the ring, from which we can find the velocity of the ring.

Now, using the conservation of momentum, we can find the velocity of the ring block system.

Let the velocity of the ring-block system be .

Then