Elastic collision in a pendulum

[Jenez]

Hello people. New here and I've got a problem here which i would appreciate some help with.

Situation :
A ball of mass 300g is attached to a massless string of 0.2m suspended at a 90 degree angle to another ball of mass 500g held by a massless string at length 0.2m.
Imagine the ball A (0.3kg) is positioned next to ball B, which are equal except for masses. Ball A is moved in a quarter of a circle motion up 0.2m, keeping it's string straight. That is the case we are examening.
The question is, what are the maximum heights ball A and B can attain after ball A is released collides with B?

We assume that this is an insulated system, meaning 100 % conserved energy and momentum.

Through PEi + KEi = PEf + KEf We achieve the velocity 1.98 m/s right before collision with ball B.

The problem arises when the total KE for the system has to be distributed correctly between ball A and B post-collision. I've reached the point where the KEi = Va final + 5/3 Vb final

How do you go about finding either one of the velocities? I know that the V of B will be greater than V of A since B has less than double the mass of A

Appreciate your help!

 

[Phlogistonian]

Use the formulas for an elastic collision.

$$p_{before} = p_{after}$$

$$KE_{before} = KE_{after}$$

That will give you 2 equations with 2 unknowns.

 

[Moetasim]

Hello there! I would like to provide some insight into your problem. First of all, this situation can be described as an elastic collision between two objects, which means that both the kinetic energy and momentum are conserved during the collision. This is due to the assumption of an insulated system, where there is no external force acting on the system.

To find the maximum heights that balls A and B can attain after the collision, we need to use the conservation of energy and momentum equations. The initial potential energy (PEi) of ball A is converted into kinetic energy (KEi) as it moves up 0.2m, and this energy is then transferred to ball B during the collision. This means that the final kinetic energy (KEf) of the system after the collision is equal to the initial potential energy of ball A.

Using the equation PEi + KEi = PEf + KEf, we can solve for the final velocities of balls A and B. Since the masses and initial velocities of both balls are known, we can then use the equation for conservation of momentum (m1v1i + m2v2i = m1v1f + m2v2f) to solve for the final velocities of both balls.

In this case, the final velocity of ball A will be less than the final velocity of ball B, as you correctly pointed out. This is because of the difference in masses between the two balls. To find the exact velocities, you will need to substitute the values into the equations and solve for the final velocities.

I hope this helps you in solving your problem. Keep in mind that in an ideal scenario, the collision between the two balls would be perfectly elastic, meaning that no energy is lost during the collision. However, in real-world situations, there may be some energy loss due to factors such as friction and air resistance. But in an insulated system, we can assume that the collision is perfectly elastic.

Good luck with your calculations! And don't hesitate to ask for further clarification if needed.