At what velocity should we bounce the ball

[dogcat]

If we drop a ball from 1.5 m it is bouncing for 3 seconds. At what velocity should we bounce the ball in order to make it reach the height of 1.5 m?

 

[Ulysees]

It's indeterminate. More variables than equations.

 

[Andy Resnick]

Interesting problem. Here's how I would solve it.

Assume the ball drops from rest and the height of each bounce is some fraction 'a' of the previous bounce height. Now you have a series solution to the trajectory which should converge, giving a total amount of time the ball is bouncing- you may need to manually truncate the series when the bounce height reaches some small fraction of the initial height. Adjust that fraction 'a' so that the total time is 3 seconds.

Now, having that fraction 'a' be known, go back and figure out what initial velocity must be given to the ball such that the first bounce will achieve a height of 1.5 m. The ball will now likely be bouncing for more than 3 seconds, tho.

 

[berkeman]

Thread moved to Homework Help. dogcat, you must show us your own work and thoughts before we can offer tutorial help. Also, the 3 seconds number does not line up well with the 1.5m initial height in your statement of the problem. Are you sure those are the correct numbers? Can you please type the full question exactly as it appears in your assignment?

What can you tell us about inelastic collisions and the loss of kinetic energy...?

 

[dogcat]

It isn't in English so I think that it wouldn't help. But it is exactly like I posted. No more data and information that's why I really don't know how to solve it. (I was also quite surprised by the 3 seconds and the 1.5 m but it is correct.)

 

[dogcat]

Nobody
Somebody PLEASE!

 

[Ulysees]

Why don't you ask that teacher what's their criteria are for termination of the bounce? Less than 1 cm height?

 

[Ulysees]

Cause normally you'd assume a coefficient of restitution A where

velocity after collision = - A * velocity before collision.

This gives an exponentially reducing height of bounce that never stops.

 

[HallsofIvy]

I would interpret this as meaning one bounce. Ulysees seems to be interpreting it as the total of "all bounces".

You can use the first piece of information to determine the "coefficient of restitution. If the ball is dropped from 1.5 m you can calculate the time until the ball hits the ground and the speed at which it hits the ground. Subtract the time from the 3 seconds to see what time is left to come back up (which is how I am interpreting a "bounce". It that is too long even at 100% restitution, it may be until the ball hits the ground again). Solve for the time until maximum height, keeping initial speed as unknown and use that to solve for the initial speed on the rebound. The ratio between that and the speed with which the ball hit the ground is the "coefficient of restitution".

Now, go back, and do the calculation with an unknown initial speed at which the ball is thrown down and, with the coefficient of restitution, set up the equation for the height to which it will rebound. Set that to 1.5 m and solve for initial speed.

 

[Littlepig]

What about with energy?, the energy lost due to coefficient is proportional with energy before hitting the ground. The ball will stop with 0 energy.
Energy in the beginning is known, will only have to know the energy needed initialy to in the end the ball reach at 1.5?!

Just a hint, not sure if it can be done..

 

[Ulysees]

HallsofIvy, do you know how plasticine bouncing on the floor just once is modeled? Maybe this is what is being asked for. But then you'd have more parameters than just the coefficient of restitution.