What are the differing consequences of two different objects having the same momentum but differing kinetic energies if they were to collide into a wall, all else held equal?

Question

If they both have the same momentum, would they move the wall ( and the planet earth) by the same amount, but the one with higher kinetic energy has the higher potential to do more deformation to the wall, depending on comparative material properties?

In: Physics

Answer 1

Momentum (p) is equal to mass times velocity (m×v).

Or p=m×v

Kinetic Energy (KE) is equal to one half the mass times the square of the velocity (1/2×m×v^2)

Or KE=1/2×m×v^2

If two objects have the same momentum but differnet kinetic energies, then we can write it as m1×v1=m2×v2 and m1×v1^2 < m2×v2^2 (since both sides are multiplied by 1/2 we can ignore that.) By solving that m1=(m2×v2)/v1 and that v1=(m2×v2)/m1 and then substituting those respectively then we can see that v1<v2 and m2<m1.

So, the object with greater kinetic energy will have less mass and more speed. Now, since both are hitting identical walls, their mass will increase by the same amount, and the speed will decrease by the same amount. But, the object with greater kinetic energy will still have greater kinetic energy. And therefore the wall will be deformed more.