# Maximum potential energy after collision

• randomgamernerd
In summary, the potential energy stored in the system during the elastic collision between a ball with kinetic energy E and a stationary ball with mass n times that of the first ball is En/(n+1). This can be derived by considering the principles of conservation of mechanical energy and conservation of linear momentum, and by using the centre of momentum reference frame.
randomgamernerd

## Homework Statement

: A ball a, moving with kinetic energy E, makes a head on elastic collision with a stationary ball with mass n times that of A. The maximum potential energy stored in the system during the collision is
a)nE/(n+1)
b)(n+1)E/n
c)(n-1)E/n
d)E/n[/B]

## Homework Equations

:Principle of Conservation of mechanical energy(PCME) and principle of conservation of linear momentum(PCLM)[/B]

## The Attempt at a Solution

: I have done the sum and my answer matches correctly...I just want to confirm if my concept is correct.
Just at the instant when potential energy of the system is maximum, the two balls are moving with equal velocities(just at that instant).
So from PCLM[/B]
mu=m(n+1)V
where u=initial velocity
V=the common velocity

Now since the collision is elastic, we can conserve ME.
so

1/2mu2=1/2m(n+1)V2+ U
where U= P.E
Also
E=1/2mu2
so from the two equations above...I got
U = En/(n+1)
I just want to assure if my concept is correct
Sorry if the thread is a duplicate one...or if I've made any grammatical error...
Thanks for the help

Looks good to me.

You could also consider using the centre of momentum reference frame, which might offer a neat alternative approach.

PeroK said:
Looks good to me.

You could also consider using the centre of momentum reference frame, which might offer a neat alternative approach.

## 1. What is maximum potential energy after collision?

Maximum potential energy after collision refers to the maximum amount of energy that an object possesses after a collision with another object. It is determined by the speed and mass of the objects involved in the collision.

## 2. How is maximum potential energy after collision calculated?

The maximum potential energy after collision is calculated using the equation E = 1/2mv2, where E is the energy, m is the mass, and v is the velocity of the object.

## 3. What factors affect the maximum potential energy after collision?

The maximum potential energy after collision is affected by the mass and velocity of the objects involved in the collision. The angle of the collision and any external forces can also impact the maximum potential energy.

## 4. Why is maximum potential energy after collision important?

Maximum potential energy after collision is important in understanding the amount of energy involved in a collision and the potential for damage or change in motion of the objects involved.

## 5. Can maximum potential energy after collision be greater than the initial kinetic energy?

Yes, maximum potential energy after collision can be greater than the initial kinetic energy if the collision is inelastic, meaning that some of the kinetic energy is converted into other forms of energy such as heat or sound.

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