Closing a door by throwing something at it

[LocalStudent]

Just say I decide to close my door by throwing a tennis ball or a lump of sticky clay at the door. Both have the same mass.

I would say throwing the lump of sticky clay would be more effective.

Is this due to the conservation of momentum or kinetic energy?
Because the clay does not bounce back and therefore all the kinetic energy of the clay goes into moving the door.. <- would this be the conservation of kinetic energy and is my reasoning correct?


Thanks

 

[chrisbaird]

It depends on your door. If the clump/ball has about the same mass as the door and friction is negligible, then, no, the elastic collision (the tennis ball) would be more effective. When the clump sticks to the door, and both swing shut, the clump still has kinetic energy because it is still moving. This means that there is still energy in the clump that has not been transferred to the door. If the door has no initial friction and starts at rest, (and the thrown object has about the same mass as the door) then all of the energy from the thrown object will be transferred to the door. After the elastic collision, the tennis ball will be at rest and the door will be moving. Think Newton's Cradle. A tennis ball is a bad visual because it is so light. A better comparison would be a basketball versus a sticky clump of clay.

 

[LocalStudent]

A tennis ball is a bad visual because it is so light. A better comparison would be a basketball versus a sticky clump of clay.

So what if you were comparing the effects of the 50g tennis ball and a 50g lump of clay?

 

[tms]

Because the clay does not bounce back and therefore all the kinetic energy of the clay goes into moving the door.

In real life some energy will go into deforming the clay, of course, but that can be ignored here. Regarding kinetic energy, after the clay sticks to the door, it will still be moving, and so it will still have kinetic energy. Just think of this as a collision in one dimension, and solve the general case elastically and inelastically.

 

[chrisbaird]

If you work it out using the classical laws of conservation of mass and conservation of energy, you will find that when one mass (the ball) collides with a second mass that is initially at rest (the door), the second mass will acquire twice the velocity in a perfectly elastic collision (bouncing) that it would in a perfectly inelastic collision (sticking). This result is exact (within classical mechanics) and general, no matter what the masses of the objects are or the initial velocity. Go ahead and work out the ratio v_elastic/v_inelastic using the conservation laws and you will find everything cancels in the end leaving only the number 2.