Momentum of Wall: 2mv Explained

In summary, the momentum of a stationary wall when a ball collides with it is 2mv due to momentum conservation. The wall may appear to be not moving, but it is actually transferring its momentum to the structure it is attached to and ultimately to the Earth. The velocity of the ball changes after colliding with the wall, resulting in a change in momentum, which must also be accounted for in order for momentum to be conserved.
  • #1
pdpax
3
0
Hi everybody,
Any one can tell me why the momentum of the wall is 2mv while a ball collides it?
 
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  • #2
pdpax said:
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.
 
  • #3
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.
 
  • #4
Sakriya said:
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?
 
  • #5
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
 
  • #6
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
 
  • #7
Sakriya said:
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.
 
  • #8
Sakriya said:
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.
 
  • #9
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.
 

1. What is the meaning of "momentum of wall: 2mv"?

The momentum of wall refers to the amount of motion or movement a wall possesses. The "2mv" component represents the mass (m) of the wall multiplied by its velocity (v), which together determine the wall's momentum.

2. Why is the momentum of a wall important to study?

Understanding the momentum of a wall is important for engineers and architects when designing buildings and structures. It helps them determine the amount of force and impact a wall can withstand, and how to properly support and reinforce it.

3. How is the momentum of a wall calculated?

The momentum of a wall is calculated by multiplying the mass of the wall by its velocity. The formula for momentum is P = mv, where P is momentum, m is mass, and v is velocity. The resulting unit for momentum is kilogram-meters per second (kg·m/s).

4. Does the momentum of a wall depend on its size?

Yes, the momentum of a wall is directly proportional to its mass. This means that a larger wall with more mass will have a greater momentum than a smaller wall with less mass, as long as they have the same velocity.

5. How does the concept of momentum apply to walls in real-life scenarios?

In real-life scenarios, the momentum of a wall is important to consider in situations where the wall may experience a force or impact, such as during natural disasters or collisions with other objects. The momentum of the wall can help determine the potential damage or impact it may have on its surroundings.

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