# Momentum of the wall

#### pdpax

Hi everybody,
Any one can tell me why the momentum of the wall is 2mv while a ball collides it?

#### Doc Al

Mentor
Any one can tell me why the momentum of the wall is 2mv while a ball collides it?
I'm not sure what you mean by 'why', but it's a consequence of momentum conservation. If a ball with momentum +mv collides elastically with a fixed wall and thus rebounds with momentum -mv, the wall (and all attached to it) must end up with an total momentum of +2mv.

#### Sakriya

Any one can tell me why the momentum of the wall is 2mv while a ball collides it?

wall is not moving.. a stationary body does not posses momentum.
When the ball strikes with +p momentum the wall gives out equal and opposite reaction of -p momentum.

#### Doc Al

Mentor
wall is not moving.. a stationary body does not posses momentum.
When the ball strikes with +p momentum the wall gives out equal and opposite reaction of -p momentum.
Are you suggesting that momentum is not conserved during the collision?

#### Swallow

suppose a ball is moving with initial velocity, v towards a wall, and it rebounds with velocity -v, then the change in momentum of the ball is -2mv, which is the same as the change in momentum of the wall, BUT the wall is held in place by the forces between it and the floor, roof etc. and thus it does not move. If there was no restraining force on the wall, it would have started to move backwards.

In other words the momentum of the wall is transferred to the whole structure (building,home etc.), and thus by extension to the earth

#### Sakriya

Are you suggesting that momentum is not conserved during the collision?
Of course it is conserved.

When ball hits the wall, the wall does not move because it is held at bottom and due to rigidity and elasticity of the material. The wall gives this back to the ball as reaction due to the action. That's why the velocity is same as it was when the ball was striking it. The wall doesn't have it's own momentum which it is imparted to the ball(it seems you suggested that), if so was true then velocity of the ball after striking would be different. That's what conservation of momentum is.... final momentum equals initial

#### Dale

Mentor
Of course it is conserved.

When ball hits the wall, the wall does not move because it is held at bottom and due to rigidity and elasticity of the material. The wall gives this back to the ball as reaction due to the action. That's why the velocity is same as it was when the ball was striking it. The wall doesn't have it's own momentum which it is imparted to the ball(it seems you suggested that), if so was true then velocity of the ball after striking would be different. That's what conservation of momentum is.... final momentum equals initial
I think you are a little confused here. The velocity of the ball after striking the wall IS different! (Speed is the same, but velocity is a vector quantity so a change in direction is a change in velocity)

Because the velocity has changed the final momentum of the ball is NOT equal to the initial momentum of the ball. Therefore, for momentum to be conserved the wall's momentum must also change.

Staff Emeritus
the wall does not move
Sure it does. It just takes the whole earth with it. You might calculate the velocity change from that and convince yourself it's not a problem.

#### J.D. Westholm

wall is not moving.. a stationary body does not posses momentum.
When the ball strikes with +p momentum the wall gives out equal and opposite reaction of -p momentum.
there is no such thing as a stationary body. if the house is firmly stuck to the ground, the earth gets the extra momentum 2mv.

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