Question

Two hover pucks collide in an off-centered collision and stick to one another via velcro. When they do so, they rotate in place. Consider what was just stated, but suppose we replace both hover pucks with pucks that are the same size as the originals but twice as massive. Otherwise, we keep the experiment the same. Compared to the pucks first mentioned, this pair of pucks will rotate A. ) twice as fast. B.) one-half as fast. C.) at the same rate. D.) one-fourth as fast. E.) four times as fast. Explain reasoning.

Answer 1

Concepts and reason

The main concepts required to solve this problem are the speed, mass, law of conservation of momentum.

Initially, write the concept and equation for the conservation of momentum. Use this concept and compare the rotational motions of the first two pucks with the second two pucks with twice the masses as that of first two pucks.

Fundamentals

Momentum can be defined as the product of mass and speed of the object.

The equation for the momentum of the an object is,

Here, m is the mass and v is the speed of the object.

Law of conservation of the momentum states, that the total momentum of the system before collision is equal to the total momentum of the system after collision.

Let the masses of the first two pucks be and .

Use the law of conservation of momentum for first pair of pucks as follows,

Here, is the initial velocity of the mass, is the initial velocity of the mass, and is the final velocity of the both combined masses after collision.

Rearrange the above equation for v.

…… (1)

Let the masses of the other two pucks whose masses doubled be as follows,

and .

These two masses have the same initial velocities as that of the first two pucks. And the final velocity of the combined two masses after collision be v’.

Use the law of conservation of momentum as follows,

Rearrange the above equation for .

Substitute for , and for in above equation.

Substitute v for from equation (1) in above equation.

The final velocity of the two pucks with double the masses, after collision is the same as that of the final velocity of the first two hover pucks after collision.

Therefore, the second pair of pucks will rotate with same speed as of the first pair of pucks.

Ans:

The second pair of pucks rates with the same rate as that of the first pair of pucks.