Defennder said:The fact that the ball is airborne for shorter periods of times after each consecutive bounce is not the reason why it doesn't count as SHM. One can envisage a hypothetical scenario where the collision of the ball with the floor is entirely elastic; no kinetic energy is lost to the floor as heat, sound etc. There is something more fundamental in the definition of SHM than that consideration.
From Wikipedia:.NoStyle said:Homework Statement
How come a bouncing ball does not exhibit SHM characteristics?
Homework Equations
no clue
The Attempt at a Solution
When I think of SHM, I don't think of contact forces. In the bouncing call case, there is a contact force present when the ball hits the ground.
Would the graph for a bouncing ball look curved as it approached it's height, but then a sharp V as it hits the ground?
(By the way, a bouncing ball that is in motion in another direction exhibits what you describe with the sharp V at the impulse of the floor changing direction.
Thanks
The main reason a bouncing ball does not exhibit SHM characteristics is because it does not follow the conditions necessary for SHM. In order for an object to exhibit SHM, it must have a restoring force that is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement. However, in the case of a bouncing ball, the restoring force (gravity) is not directly proportional to the displacement and also changes direction as the ball bounces, making it impossible for the ball to exhibit SHM.
In theory, it is possible for a bouncing ball to exhibit SHM if it meets the necessary conditions. This would require the ball to have a perfectly elastic surface, constant gravitational force, and a perfectly flat and level surface to bounce on. However, in real-world scenarios, these conditions are rarely met, so a bouncing ball typically does not exhibit SHM.
Air resistance plays a significant role in a bouncing ball's motion. As the ball bounces, it experiences air resistance which causes it to lose energy and therefore bounce lower with each subsequent bounce. This is why a ball will eventually come to rest on the ground, rather than bouncing indefinitely in a perfect SHM pattern.
Technically, yes, a bouncing ball can be considered a form of periodic motion because it repeats the same motion over and over again. However, it is not considered simple harmonic motion since it does not follow the necessary conditions for SHM.
Several factors can affect the bounce of a ball, including the material and elasticity of the ball, the surface it bounces on, and external forces like air resistance and friction. The height and angle at which the ball is dropped can also affect its bounce. Additionally, factors like temperature and air pressure can also play a role in the bounce of a ball.