Inelastic collision of ball drop

In summary, a ball is dropped from rest at the top of a 6.10m-tall building, falls straight downward, collides inelastically with the ground, and bounces back. Each time the ball bounces, it loses 10% of its kinetic energy. To reach a window sill 2.44m above the ground, the ball can make a maximum of 3 bounces. This is calculated using the equation 0.9^n*h_o = h, where n is the number of bounces and h_o is the initial height of the ball.
  • #1
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a ball is dropped from rest at the top of a 6.10m-tall building, falls straight downward, collides inelastically with the ground, and bounces back. the ball loses 10.0% of its kinetic energy every time it collides with the ground. how many bounces can the ball make and still reach a window sill that is 2.44m above the ground?

all that i know is that K=1/2mv^2
 
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  • #2
If the collision is perfectly elastic, the ball will reach its original height after each bounce. but since each bounce, 10% of its energy is lost, (90% remaining), it will only reach 90% of the last height it acheived.

For this question, I don't think it is necesary to actually calculate any kinetic energies or momentums, ...

Can you think of an equation that will relate the rebound height of the ball to the number of bounces that have occured.
 
  • #3
Consider that the potential energy at the top of the bounce is converted to the kinetic energy at the bottom - after the first bounce we have this amount of kinetic energy left then [itex]0.9mgh_o[/itex]. This kinetic energy is then converted into potential energy at the top of the bounce [itex]mgh[/itex] for the ball reaching a height [itex]h[/itex] with this available kinetic energy. After the next bounce the total kinetic energy available for the next peak will therefore be [itex]0.9^2mgh_o[/itex]. For n bounces it will therefore be [itex]0.9^nmgh_o[/itex]. The equation therefore becomes
[tex]0.9^nh_o=h[/tex]
quite simple is'nt it?
 
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What is an inelastic collision?

An inelastic collision is a type of collision where there is a loss of kinetic energy. This means that the total energy of the system before and after the collision is not conserved, as some energy is lost to other forms such as heat or sound.

How is the collision of a ball drop different from other types of collisions?

In the collision of a ball drop, the ball is dropped from a certain height and collides with the ground. This type of collision is different from others because the ball is not colliding with another object of the same mass, but rather with a much larger and stationary object (the ground).

What factors affect the inelastic collision of a ball drop?

The main factors that affect the inelastic collision of a ball drop are the mass and velocity of the ball, as well as the height from which it is dropped. These factors determine the amount of kinetic energy the ball has before the collision and how much energy is lost during the collision.

How is the coefficient of restitution related to the inelastic collision of a ball drop?

The coefficient of restitution (COR) is a measure of the elasticity of a collision. In the case of a ball drop, a lower COR indicates a more inelastic collision, meaning that more energy is lost. A higher COR indicates a more elastic collision, where less energy is lost.

Why is the inelastic collision of a ball drop important in physics?

The inelastic collision of a ball drop is important in physics because it helps us understand the principles of energy conservation and the transfer of energy between different forms. This type of collision is also commonly used in real-world applications, such as in sports and engineering, making it a valuable concept to understand.

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