Conceptual understanding of moment transfer for bouncing ball

In summary, the conversation discusses the concept of a ball of mass m bouncing against a hard floor in an elastic collision. The momentum in the system is conserved, with the floor gaining momentum while the ball loses momentum. There is a transfer of momentum between the ball and the floor before and after the impact, and the ball's elastic energy converts back to kinetic energy as it regains its form. The force between the ball and the floor changes over time, with an initial decrease and then an increase before and after the ball reaches maximum compression. The conversation also raises questions about the force and momentum at specific instants in the collision.
  • #1
Physics.1o1
1
0
Hi,

I am trying to wrap my head around what happens when a ball of mass m bounces against a hard floor. I assume a system that includes the ball and the floor (and eventually the entire planet) and an elastic collision. Before the ball hits the floor it has a momentum of mv. After the bounce the ball momentum change to -mv (that is changes by -2mv) and the floor momentum increases by +2mv. This way the momentum in the system is conserved.

At the instant just before the impact, t_a, the boll momentum is +mv and floor momentum is 0. At time t_a the ball touches the floor. According to Newton's 3rd law, the ball exerts a force F on the floor and the floor responds with a corresponding force -F (a force of equal magnitude, but in opposite direction). The ball starts compressing due to the force from the floor, loosing velocity and converting its kinetic energy into elastic (potential) energy. At the instant t_0 the ball velocity is 0 and maximum compression was achieved. Between t_a and t_0 an amount of +mv of momentum is transferred to the floor due to the force from the ball and -mv momentum is transferred from the floor to the ball due to the force from the floor. Thus, the floor momentum has increased by mv and the ball momentum is 0. After t_0, the ball's elastic energi begins to convert back to kinetic energi while the ball regains form. This results in a force F exerted by the ball on the floor and corresponding force -F from the floor that accelerates the ball upward. At instant t_b, when the ball looses contact with the floor, the floor has gained another +mv momentum and the ball lost the same amount. Consequently, the floor has now +2mv momentum and the ball has -mv momentum. Is this an accurate (albeit idealistic) explanation?

Also, am I correct in assuming that the force F decreases to 0 between t_a and t_0 and increases from 0 to F between t_0 and t_b? I am bit conflicted about what happens at t_0. At that instant I would think the ball still exerts a force F=mg on the floor and a corresponding force is exerted by the floor on the ball. In that case, F never decreases below mg... Hopefully somebody can help with a good explanation :-)
 
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  • #2
Physics.1o1 said:
Also, am I correct in assuming that the force F decreases to 0 between t_a and t_0 and increases from 0 to F between t_0 and t_b?
No, the other way around

Physics.1o1 said:
I am bit conflicted about what happens at t_0. At that instant I would think the ball still exerts a force F=mg on the floor
No, more than mg

Physics.1o1 said:
F never decreases below mg
It does, around t_a and t_b.
 

Related to Conceptual understanding of moment transfer for bouncing ball

1. What is the concept of moment transfer for a bouncing ball?

The concept of moment transfer for a bouncing ball refers to the transfer of energy and momentum between the ball and the surface it bounces off of. When the ball hits the ground, it compresses and then bounces back up, transferring energy from the ground to the ball and causing it to bounce.

2. How is moment transfer related to the height and speed of a bouncing ball?

The moment transfer is directly related to the height and speed of a bouncing ball. The higher the ball is dropped from, the greater the potential energy it has, resulting in a higher bounce. Similarly, a ball dropped with more speed will have a greater momentum and will thus bounce higher.

3. What factors affect the moment transfer for a bouncing ball?

The moment transfer for a bouncing ball can be affected by various factors such as the surface it bounces off of, the elasticity of the ball, and any external forces acting on it. A harder surface will result in a higher moment transfer, while a softer surface will absorb more energy and result in a lower bounce.

4. How does the angle of impact affect the moment transfer for a bouncing ball?

The angle of impact can also affect the moment transfer for a bouncing ball. If the ball hits the surface at a shallow angle, it will have a longer contact time with the surface and will transfer more energy, resulting in a higher bounce. On the other hand, a steeper angle of impact will result in a shorter contact time and a lower bounce.

5. Can the moment transfer for a bouncing ball be calculated?

Yes, the moment transfer for a bouncing ball can be calculated using the laws of conservation of energy and momentum. By taking into account the mass, initial velocity, and height of the ball, as well as the properties of the surface it bounces off of, the moment transfer can be determined. However, factors such as air resistance and the deformation of the ball may make the calculation less accurate.

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