Bouncing a ball force calculation

In summary, the speed component normal to the plane (such as the floor) gets reversed when a ball bounces off of it. This change in momentum is caused by a force that pushes the ball away from the wall over a certain period of time. The force can be calculated based on factors such as the rigidity of the wall and the speed of the ball. To simulate this in a physics simulation, one can use a mass and spring model with equations for velocity and position to create a parabolic motion similar to that of a bouncing ball. The force and acceleration can be adjusted to achieve the desired effect. Additionally, considering energy loss in the simulation can make the bouncing more realistic.
  • #1
daniel_i_l
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When a ball bounces into something like the floor the component of the speed normal to the plane (for example the floor) gets reversed.
I'm trying to program a physics simulation were there are, among other things, balls bouncing off walls and stuff. Now I know that I could simply reverse the speed component as I explained above to make the ball bounce but this is somewhat af a "hack", what I want to know is how it "really" happens - in terms of forces and stuff. The ball changes it's momentum which means that there is some force that pushes the ball from the wall over a certain time - impulse. How do I calculate this force (by perimiters such as the rigedness of the wall, speed of the ball...) and how do you know when to apply it and when to stop?
Thanks.
 
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  • #2
If it were me, I would start with the mass and spring model. Let the velocity decrease linearly to zero then increase back to where it was, but in the other direction. Keep the slope the same no matter how fast the ball approaches the wall. This will create the parabolic motion that a bouncing ball in contact with the floor in slow motion would so closely resemble.

Relevant Newton's Equations:

(velocity) = (initial velocity) + (acceleration) x (time)

(Position) = (initial position) + (initial velocity) x (time) +
1/2 (acceleration) x (time)^2

The acceleration is of course in reality determined from the force and the mass, and the force is determined from Hooke's Law F = -kx where k is the spring constant which you can play with, but you could also just play with the acceleration until it looks right.

Are you going to consider energy loss? i.e. will the ball eventually stop bouncing?
 
  • #3


I would like to commend your interest in understanding the physics behind the bouncing of a ball. You are correct in stating that the change in momentum of the ball is due to a force acting on it. In this case, the force is a normal force exerted by the surface it bounces off of, which is equal in magnitude and opposite in direction to the force exerted by the ball on the surface.

To calculate this force, you would need to consider the rigidity of the surface, as well as the speed and mass of the ball. The force would be equal to the change in momentum of the ball over a certain time period, also known as the impulse. This can be calculated using the equation F = Δp/Δt, where F is the force, Δp is the change in momentum, and Δt is the time interval over which the change occurs.

In terms of when to apply this force and when to stop, it would depend on the specific conditions of your simulation. Generally, the force would be applied as soon as the ball makes contact with the surface and would continue until the ball leaves the surface. This would depend on factors such as the elasticity of the ball and surface, as well as any other external forces acting on the ball.

I would also suggest looking into the concept of coefficient of restitution, which is a measure of the elasticity of a collision between two objects. This can help you better understand the behavior of the ball during a bounce and can be incorporated into your calculations.

Overall, it is important to understand that the bouncing of a ball is a complex phenomenon and there are many factors that can influence it. By considering the principles of momentum and forces, as well as other factors such as elasticity and surface properties, you can create a more accurate and realistic simulation. I wish you all the best in your endeavors.
 

1. How is the force of a bouncing ball calculated?

The force of a bouncing ball is calculated using the equation F = ma, where F is the force, m is the mass of the ball, and a is the acceleration due to gravity.

2. What factors affect the force of a bouncing ball?

The force of a bouncing ball is affected by the mass of the ball, the height from which it is dropped, and the surface on which it bounces. Air resistance and spin on the ball can also affect the force.

3. How do you calculate the height of a bounce for a ball?

The height of a bounce for a ball can be calculated using the equation h = (e*h0), where e is the coefficient of restitution and h0 is the initial height of the ball.

4. What is the coefficient of restitution?

The coefficient of restitution is a measure of how much energy is conserved during a collision. It is a dimensionless number between 0 and 1, where 0 represents no energy conservation and 1 represents perfect energy conservation.

5. How does the surface affect the force of a bouncing ball?

The surface on which a ball bounces can affect the force by changing the amount of energy that is absorbed or transferred during the collision. A softer surface, such as a rubber mat, will absorb more energy and result in a lower bounce compared to a harder surface, such as concrete, which will transfer more energy and result in a higher bounce.

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