How to Calculate KE and Momentum of a Bouncing Ball?

[maltese]

Bouncing Ball KE and momentum??

Does anyone know how to calculate the KE and momentum of a bouncing ball?

My quadratic equation is -4.113^t2+19.7t-22.72

The bounce begins at t=1.90s
the bounce ends at t=2.85s
The maximum height from my graph is (i think).8m.

For this exp I don't need the mass as I am trying to derive the following KE/m and p/m both before and after impact.
I am so confused;
do I plug in the start time of the bounce into the quadratic equation? then what? i nkow PE is related to this somehow, so should I be using gh to find KE/m?
can someone please help?

 

[jbsteele]

The equation you have is the vertical position of the ball as a function of time. To get the kinetic energy and momentum of the ball at any given time, you will first need to calculate the velocity of the ball at the given time. You can do this by taking the derivative of the quadratic equation with respect to time. This will give you the velocity equation. Then, the kinetic energy of the ball is equal to 1/2mv2, where m is the mass of the ball, and v is the velocity of the ball at the given time. The momentum of the ball is equal to mv, where m is the mass of the ball and v is the velocity of the ball at the given time. You can plug in the start time and the end time into your velocity equation to calculate the velocity of the ball at each time, then plug the velocity into the kinetic energy and momentum equations to calculate the KE/m and p/m both before and after impact.

 

[Moetasim]

I would first clarify the units of the given equation and make sure they are consistent with the units of KE and momentum, which are Joules (J) and kilogram meters per second (kg·m/s), respectively. Then, I would suggest breaking down the problem into smaller parts and using the equations for KE and momentum to calculate these values.

To calculate KE, you can use the equation KE = 1/2 * m * v^2, where m is the mass of the ball and v is the velocity. Since the mass is not provided, you can assume a standard value (e.g. 1 kg) or use the ratio of KE/m to compare before and after impact.

To calculate momentum, you can use the equation p = m * v, where m is the mass and v is the velocity. Again, you can use a standard value for mass or use the ratio of p/m to compare before and after impact.

To find the velocity, you can use the equation v = u + at, where u is the initial velocity (in this case, it would be the velocity at the start of the bounce), a is the acceleration (which can be calculated using the given quadratic equation), and t is the time. You can use the start time of the bounce as t=0 and plug in the end time to find the velocity at the end of the bounce.

As for the maximum height, you can use the equation PE = m * g * h, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height. You can use the given maximum height to solve for the mass and then use that value in the KE and momentum equations.

I hope this helps you with your calculations. It may be helpful to create a table or graph to organize your data and calculations. Good luck!