The force on the ball is the same as what?Liam Lau said:Homework Statement
Why does a ball bounce less and less high, even though the force exerted by the ground on the ball is the same, due to Newton's third law.
According to this, as energy is conserved, the ball should reach the same height again, and keep on bouncing till the same height. This is true for the ideal world. The question asks why the height gets reduced after each successive bounce or collision to be precise. This is due to the properties of the material the ball is made of, and the the coefficient of restitution of that material. It includes the energy dissipated to the sorroundings.andrevdh said:As it rises its kinetic energy is converted into gravitational potential energy.
At the top all of the kinetic energy is converted into potential energy and its
speed is momentarily zero since kinetic energy is zero. So the maximum
height it reaches is determined by its kinetic energy at the bottom.
Liam Lau said:Thanks for all the comments, but there is one thing I am confused with. Does the height of the ball bounced not depend on the force exerted of the ball when it is thrown at the ground? The point I'm trying to make is that doesn't Newton's third law state the Force of the ball hitting the ground is equal to the ground pushing back at the ball, I was just wondering why this doesn't affect the height the ball bounces back.
Thanks, this clarified the confusion I had.jbriggs444 said:The force the ground exerts on the ball is equal at all times to the force that the ball exerts on the ground. But that is irrelevant. The force that the ball exerts on the ground affects the ground. It does not affect the ball. The only force that is relevant is the force that the ground exerts on the ball.
As the ball hits the ground and compresses, the force exerted on the ball by the ground is slowing the ball down. Eventually the ball reaches its low point and starts rebounding upward. From that point on, the force exerted on the ball by the ground is speeding the ball up.
The relevant question is whether the [time integral of] the force of the ground on the ball during the compression is equal to the [time integral of] the force of the ground on the ball during the rebound. In general, the two will not be equal. Instead, the force during the rebound will be somewhat less. Often the ratio between the two will be more or less constant. That constant is called the "coefficient of restitution".
When a ball bounces, it undergoes a process called elastic collision. This means that the ball's energy is transferred from kinetic energy (energy of motion) to potential energy (energy of position) as it compresses upon impact. However, some of this energy is lost as heat and sound, resulting in a decrease in the ball's overall energy and a lower bounce height.
The height of a ball's bounce is affected by several factors, including the material and stiffness of the ball, the surface it bounces on, and the force and angle at which it is dropped. These factors influence the amount of energy lost during the bounce and can result in varying bounce heights.
The height of a ball's bounce depends on its material and stiffness. For example, a rubber ball will bounce higher than a foam ball due to its greater elasticity. Additionally, a ball with a higher initial velocity will have more energy to transfer during the bounce, resulting in a higher bounce height.
The height of a ball's bounce can be predicted using mathematical equations that take into account factors such as initial velocity, mass, and surface properties. However, controlling the bounce height can be difficult as it is influenced by external factors such as air resistance and surface imperfections.
If a ball were to bounce on a perfectly elastic surface with no energy loss, it would continue to bounce infinitely with the same height. However, this scenario is not possible in real life as energy is always lost in the form of heat and sound during a bounce.