What Factors Affect the Bouncing of Balls on Different Surfaces?

[bruceleeroy]

Okay. Well I'm in high school and I made an account on this forum to see if I can get some insight on an interesting phenomena my teacher showed me.

He asked us which way a tennis ball would bounce if he bounced it on the floor at an angle and let it hit the bottom of a table, and gave us three choices:

1. the ball will bounce, hit the bottom of the table, and come out the other side
2. the ball will bounce, hit the bottom of the table, and continue to hit the bottom of the table (stay under the table)
3. the ball will bounce, hit the bottom of the table, and come back to him

the ball bounced through, then he tried several other balls, and the results varied. the golf ball also went through, the lacrosse ball bounced back, the basketball stayed under the table. We asked him to vary the angle, spin, and speed for each ball, but the each ball was consistent in what happened when it was thrown. Sorry if i left any information out, but any ideas as to why the balls bounce the way they do?

 

[WhoWee]

We asked him to vary the angle, spin, and speed for each ball, but the each ball was consistent in what happened when it was thrown.

Can you clarify this sentence?

 

[Alkaline101]

It depends on the what it's made of, size, and texture.

Have you ever spun a bouncy ball one direction and after it hit the floor it spun in a different direction?

Well, the basketball does the same thing. Since the basketball has a leathery skin it creates more friction as it hits the ground causing it to spin in the opposite direction, this opposite spin will counteract the direction it is traveling in and stop the ball.

The golfball's outside, however, is made of plastic. Plastic is smoother which causes less friction as it hits the ground. As a result, it will slide a small amount as it hits the ground and the bottom of the table. That is why the golfball will eventually come out at the other side.

 

[sijokjoseph]

Even the one dimensional case is little bit complicated.
That means the ball is bouncing vertically on the table.
The dynamics of the ball greatly depends on the dissipation effect, means how much energy is losing after each bounce.
There are different situations if the dissipation is zero you will get some periodic bounces. This is called locking mechanism in which the ball bounces with almost constant amplitude.
The second mechanicm is chattering, the ball bounces with a small amplitude but it make a lot of collisions in small interval of time. I think you may have observed it when you do the experiments with some steel balls on a table, you hear some nice krrrrrrr sound.

 

[pallidin]

I've done this. I think it was with a golf ball years ago. I work at a golf club.
Anyway, the room I was in had a concrete floor(we have a new clubhouse now), with a plywood shelf about 3 feet above, essentially level with the floor.

I recall that with, I think, a forward spin, the ball hit the concrete, rebounded at a forward angle, hit the plywood above, rebounded to the floor, then came back to me.

Can't remember if it was a forward or backwards spin, but it was repeatable.

 

[rcgldr]

There are two components to how elastic the collision is, linear and angular (rate of rotation) in addition to coefficient of friction. A billard ball could have a low coefficient of friction depending on the surface of the floor, so linearly they are nearly elastic, and angularly there isn't much change because of the low coefficient of friction. These will tend to bounce out the other side of the table. A "superball" is nearly elastic both linearly and angulary, and it has a high coefficient of friction, so it would tend to return back to the same side of the table. A basketball has a decent coefficent of friction, but it's not that angularly elastic, so it would tend to stay under the table (size would also be a factor). Depending on the coefficient of friction between tennis ball and the surface of the floor, a tennis ball could also stay under the table or go out the other side.

 

[pallidin]

Correction to my post. I now remember that it was done with a "super ball" that I found and was playing with.
Sorry for any confusion.

 

[Rap]

When a ball hits the floor at an angle, it will acquire a spin such that when it hits the top of the table, the spin will tend to oppose its horizontal motion. Likewise, when it hits the top of the table, it will get a spin such that when it hits the floor the spin will oppose its horizontal motion. The more friction there is between the ball and floor/table, the stronger this effect will be. That means for low-friction situations (dense, slippery golf ball) the effect will be small and the ball will travel through. For high friction situations (low density, rubber superball or basketball) it will get trapped under the table, or it may bounce back after one bounce on the floor and one bounce on the table.

 

[DaveC49]

There are two components to how elastic the collision is, linear and angular (rate of rotation)

rcgldr,

What are the two components of elasticity you refer to? Elasticity relates to the extent to which a material can undergo deformation and return to its previous shape. It can be different in different directions (anisotropic) in some materials but I don't think this is what you meant.

The process of deformation in an inelastic material involves the dissipation of energy.

Friction is a measure of the ability of two surfaces to "stick" to each other or the resistance to them sliding against each other.

The ball has both linear and angular (spin) momentum . The elasticity of and friction between the colliding surfaces influence the way in which the momentum is transferred from before the collision to the after collision situation.

Consider initially the case with no spin. The momentum normal to the surface is affected by the elasticity of the material. If the materials are perfectly elastic, then the normal momentum component is reflected from the surface, when the surface deformations of the wall and the ball return to their original shapes. If either of the materials is inelastic, then the normal momentum component is reduced by the amount of the change of momentum as a result of the absorption of energy by the inelastic processes. The tangential component is affected by the friction between the surfaces. If friction is zero, then it is not affected, but is reduced if the friction is non-zero. These changes in the linear momentum control the direction of motion after the collision with a wall.

If we add spin into the system, angular momentum has to be resolved into normal and tangential components (normal and tangential to the direction of the linear motion) and the effects of friction and elasticity of both the materials on all of these has to be considered considered. Friction will have the effect of reducing the angular momentum of tangential angular momentum components normal to the direction of linear motion.

In practice we have to apply the conservation of linear and angular momentum and conservation of total energy of the system, including the energy transformed to heat and sound in the materials (and the air).

The deformation of the ball and wall will have an effect on the area of contact which will increase the frictional effects on the momentum changes (linear and angular) as the area of contact increases. It may also produce changes in the angle of contact over the area of contact which have to be considered. As none of this takes place instantaneously, these processes have to be integrated over the time of contact to calculate the final motion.

A second bounce is in practice no different from the first bounce. The output linear and angular momentum of the first bounce become the input for the second and so on until the energy is totally absorbed or the walls end or both.

 

[rcgldr]

There are two components to how elastic the collision is, linear and angular (rate of rotation).

What are the two components of elasticity you refer to?

Elasticity related to compression deformation versus shear deformation. They're not the same, especially in compound objects like a golf ball (solid core) or basketball (air core). Examples of this are exhibited by the various brands of table tennis sheets (the sponge and rubber component), which have varying amounts of friction, and elasticity in compression and shear. In the case of "offensive" oriented sheets with similar friction, some have more speed (compression elasticity) while others have more spin (shear elasticity). The effect when playing with these type of paddles is similar to the experience of a superball, which also has a high amount of friction, compression, and shear elasticity.

 

[DaveC49]

rcgldr,

Agree completely they are not the same thing, but are components of the elasticity tensor which describes the behavior of a material in 3D. A full 3D computer model would be interesting to play with. The astronomers will have one for modelling planetary and asteroid collisions.