How to find resulting velocity in a perfectly elastic collision?

AI Thread Summary
In a perfectly elastic collision, the conservation of momentum and kinetic energy must both be applied to find the resulting velocities. The initial momentum equation m×u = m×v1 + M×v2 is valid, but the final velocities v1 and v2 must be expressed in terms of known variables to solve the problem correctly. The discussion emphasizes that v1 cannot remain in the final answer since it is unknown, and another equation, specifically for energy conservation, is necessary to eliminate it. Without incorporating kinetic energy conservation, the calculations will yield incorrect results. Properly applying both conservation principles is crucial for determining the correct velocities after the collision.
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Homework Statement
A particle of mass m travelling with velocity u collides elastically and head-on with a stationary particle of mass M. Which expression gives the velocity of the particle of mass M after the collision.
Relevant Equations
Momentum=Mass×Velocity
Using principle of conservation of momentum:
m×u=m×v1 + M×v2
Where m=mass of moving particle in the beginning
u=Initial velocity of particle m
v1= final velocity of particle m
v2=velocity of object M
m×u-(mv1)=Mv2
(mu-mv1)÷M=v2
My answer is this (mu-mv1)÷M
However, it is nowhere close to the correct answer. Kindly tell where I am going wrong in the calculation.
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You should not have v1 in the answer since that is also unknown. You have not used that the collision is perfectly elastic.
 
haruspex said:
You should not have v1 in the answer since that is also unknown. You have not used that the collision is perfectly elastic.
I have used V1 im the equation because the initial momentum is equal to final momentum and V1 is a part of the final momentum.
 
haha0p1 said:
I have used V1 im the equation because the initial momentum is equal to final momentum and V1 is a part of the final momentum.
There's nothing wrong with it as an equation, but it is not acceptable as an answer. Only m, M and u are allowed. To eliminate v1 you need another equation, the equation for energy conservation.
 
Using principle of conservation of momentum:
mu=(m×v-u)+M×v
mu-m(v-u)=M×v
-mv÷M=v

Note:
m=mass of the initially moving object
v=velocity of object woth mass M
x-u=Velocity of object m after the collision

I have used a different method but I am still getting a wrong answer.
 
If the different method does not include kinetic energy conservation as @haruspex suggested, you will keep getting a wrong answer. The initial momentum conservation equation you had
haha0p1 said:
m×u-(mv1)=Mv2
is correct so leave it alone. Be sure to use subscripts to avoid confusion.
 
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