# Elastic collision between two balls with different masses

• kshitij
In summary, In an elastic collision, both momentum and energy is conserved. However, if we use conservation of energy, we get two different answers. One answer is that the ratio m2/m1 is 2, while the other answer is 8. I don't know why this is, but it is an incorrect answer.
kshitij
Homework Statement
A ball of mass m1 is moving with velocity 3v. It collides head on elastically with a stationary ball of mass m2 . The velocity of both the balls become v after collision. Then the value of the ratio m2/m1 is
Relevant Equations
Conservation of momentum, Conservation of energy
Since in an elastic collision, both momentum and energy is conserved,
P(initial)=P(final)
m1(3v)=m1v+m2v
m2/m1=2
Which was the given answer but if we use conservation of energy,
K.E(initial)=K.E(final)
1/2*m1*(3v)^2=1/2*m2*v^2+1/2*m1*v^2
m2/m1=8
Why do we get two different answers and why doesn't conservation of energy gives us the right answer here?

kshitij said:
Homework Statement:: A ball of mass m1 is moving with velocity 3v. It collides head on elastically with a stationary ball of mass m2 . The velocity of both the balls become v after collision. Then the value of the ratio m2/m1 is
Relevant Equations:: Conservation of momentum, Conservation of energy

Since in an elastic collision, both momentum and energy is conserved,
P(initial)=P(final)
m1(3v)=m1v+m2v
m2/m1=2
Which was the given answer but if we use conservation of energy,
K.E(initial)=K.E(final)
1/2*m1*(3v)^2=1/2*m2*v^2+1/2*m1*v^2
m2/m1=8
Why do we get two different answers and why doesn't conservation of energy gives us the right answer here?
Why do you think energy is conserved in this collision?

PeroK said:
Why do you think energy is conserved in this collision?
A perfectly elastic collision is defined as one in which there is no loss in kinetic energy in the collision. That's what I've been taught.

kshitij said:
A perfectly elastic collision is defined as one in which there is no loss in kinetic energy in the collision. That's what I've been taught.
Why do you think this is a perfectly elastic collision?

kshitij
PeroK said:
Why do you think this is a perfectly elastic collision?
The question states that they collide elastically but if you're saying that they didn't include the word perfectly then I understand.

kshitij said:
The question states that they collide elastically but if you're saying that they didn't include the word perfectly then I understand.
Sorry, I missed that. The question is wrong.

Another way to describe an elastic collision is that the "separation speed" is conserved. I.e. the speed at which the objects are moving apart after the collision is the same as the speed at which they are moving together before the collision. With a bit of algebra you can show that is the same as conservation of kinetic energy.

In this case, as the balls stick together after the collision, it cannot be elastic. In fact, when they stick together is is called a totally inelastic collision. And, again with a bit of algebra, you can show that this represents the maximum possible energy loss.

In short, you cannot have conservation of energy in this scenario.

You always have conservation of momentum. So, in this case the solution is simply to use that.

kshitij
PeroK said:
Sorry, I missed that. The question is wrong.

Another way to describe an elastic collision is that the "separation speed" is conserved. I.e. the speed at which the objects are moving apart after the collision is the same as the speed at which they are moving together before the collision. With a bit of algebra you can show that is the same as conservation of kinetic energy.

In this case, as the balls stick together after the collision, it cannot be elastic. In fact, when they stick together is is called a totally inelastic collision. And, again with a bit of algebra, you can show that this represents the maximum possible energy loss.

In short, you cannot have conservation of energy in this scenario.

You always have conservation of momentum. So, in this case the solution is simply to use that.
I thought the catch was that every collision is elastic but only in perfectly elastic collisions coefficient of restitution(e) is exactly equal to 1 and in perfectly inelastic collision, e=0.

But as you said that they move together with the same velocity after collision so here e=0 so they should write perfectly inelastic instead of elastic in the question but anyway thanks for helping me.

kshitij said:
I thought the catch was that every collision is elastic but only in perfectly elastic collisions coefficient of restitution(e) is exactly equal to 1 and in perfectly inelastic collision, e=0.

But as you said that they move together with the same velocity after collision so here e=0 so they should write perfectly inelastic instead of elastic in the question but anyway thanks for helping me.
Elastic is unambigously the same as perfectly elastic: no loss of KE.

Inelastic has more variety, in that there is a range of KE than may be lost, up to the maximum amount where the objects stick together, which is called perfectly inelastic.

https://en.wikipedia.org/wiki/Elastic_collision

https://en.wikipedia.org/wiki/Inelastic_collision

SilverSoldier and kshitij
"The velocity of both the balls become v after collision"
It occurred to me that they might mean (or perhaps even wrote) speed rather than velocity. But it doesn't help, merely creating the extra possible solution to the momentum equation m2 =4m1.

## 1. What is an elastic collision between two balls with different masses?

An elastic collision between two balls with different masses is a type of collision where both balls bounce off each other without any loss of kinetic energy. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

## 2. What factors affect the outcome of an elastic collision between two balls with different masses?

The outcome of an elastic collision between two balls with different masses is affected by the masses of the balls, their velocities, and the angle at which they collide. The elasticity of the balls and any external forces acting on them can also impact the outcome.

## 3. How is momentum conserved in an elastic collision between two balls with different masses?

In an elastic collision between two balls with different masses, momentum is conserved. This means that the total momentum of the system before the collision is equal to the total momentum after the collision. This is because there are no external forces acting on the system during the collision.

## 4. What is the formula for calculating the velocities of two balls after an elastic collision with different masses?

The formula for calculating the velocities of two balls after an elastic collision with different masses is: v1f = [(m1-m2)v1i + 2m2v2i] / (m1+m2) and v2f = [(m2-m1)v2i + 2m1v1i] / (m1+m2), where m1 and m2 are the masses of the two balls, v1i and v2i are the initial velocities of the balls, and v1f and v2f are the final velocities of the balls.

## 5. Can an elastic collision between two balls with different masses result in one ball stopping completely?

No, in an elastic collision between two balls with different masses, both balls will always have non-zero velocities after the collision. This is because the total kinetic energy of the system is conserved, so even if one ball has a much larger mass, it will still have some velocity after the collision.

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