Is the Change in Momentum the Same When Dropping a Glass on Concrete vs Carpet?

[Revengeance]

Homework Statement

If you drop a drinking glass onto a concrete floor, the glass will very likely break. But if you dropped the same glass from the same height onto a carpeted floor, it might not break. Is the change in momentum of the glass the same in both cases? EXPLAIN your response.

Homework Equations

p = mv

The Attempt at a Solution

The change in momentum will not be the same in both cases. Change in momentum is defined by p = f * t. Time elapsed will be the same in both cases, but the force exerted will not. The concrete ground will exert a larger force on the drinking glass, than the carpet ground will. Therefore having a larger change in momentum of the glass is not the same in both cases ( the force exerted by the concrete ground sounds absolutely wrong, but I thought it was correct at first)

 

[SammyS]

Homework Statement

If you drop a drinking glass onto a concrete floor, the glass will very likely break. But if you dropped the same glass from the same height onto a carpeted floor, it might not break. Is the change in momentum of the glass the same in both cases? EXPLAIN your response.

Homework Equations

p = mv

The Attempt at a Solution

The change in momentum will not be the same in both cases. Change in momentum is defined by p = f * t. Time elapsed will be the same in both cases, but the force exerted will not. The concrete ground will exert a larger force on the drinking glass, than the carpet ground will. Therefore having a larger change in momentum of the glass is not the same in both cases ( the force exerted by the concrete ground sounds absolutely wrong, but I thought it was correct at first)

That is NOT the definition of change in momentum. Momentum, p, is given by mv . Change in momentum is p₂ - p₁,
which is equal to mv₂ - mv₁.

It is also true that, consistent with Newtons 2nd Law, change in momentum is equal to the impulse for the net force, F_net⋅t .

For your situation, it would seem that v₂ - v₁ is the same in both situations. Right ?

 

[SDewan]

You can also use the fact that the force exerted by the glass on the carpet will get dispersed in the "padding" of the carpet. When the glass hits the carpet, the energy is absorbed as the glass contacts the carpet and it’s “padding”. As the “padding” of the carpet in compacted by the glass, the force of energy is absorbed and dispersed into the carpet. However, if the glass drops to the concrete, all the energy is concentrated on the point of impact with dispersion causing the force to react and go back into the glass causing a “break factor” greater than what the glass can actually withstand.