Very heavy particle collides with a very light particle

[coconut62]

Question:
A heavy particle of mass m1, moving with speed u, makes a head-on collision with a light particle of mass m2, which is initially at rest. The collision is perfectly elastic, and m2 is very much less than m1, Describe the motion of the particles after the collision.

Answer:
Heavy particle's speed is practically unchanged; light particle moves with speed 2u, in same direction as the incident heavy particle.

My question:
Why must the speed of the light particle be 2u?

Lets say I take a 10kg particle colliding with a 0.1kg particle.

using Principle of Conservation of Momentum,
10u = 10Va + 0.1Vb

...then I take Va to be very small.
...
...

No matter how I see, I still cannot see why it's 2u :grumpy:

 

[ehild]

Why do you take the velocity of the big particle after the collision very small?

Find the expressions for the velocities after the collision, using also conservation of energy and take the limit m2/m1 --->0.

ehild

 

[coconut62]

Why do you take the velocity of the big particle after the collision very small?

Because "heavy particle's speed is practically unchanged".

Find the expressions for the velocities after the collision, using also conservation of energy and take the limit m2/m1 --->0.

I substituted V1 and V2 into the energy equation and end up in a long-winded equation without being able to get the answer.

 

[ehild]

Because "heavy particle's speed is practically unchanged".

If it is unchanged and remains u, how does it become very small?

I substituted V1 and V2 into the energy equation and end up in a long-winded equation without being able to get the answer.

You have two equations with two unknowns - aren't you able to solve? Express V1 in terms of V2 and substitute into the energy equation. Solve for V2.

ehild

 

[coconut62]

I got it, thank you.

 

[benny.arimon]

Hi ehild and coconut62,

I work on this since yesterday, yet i can not solve this question.
Would you mind showing me how to solve it?

Thanks.

 

[J Hann]

Hi ehild and coconut62,

I work on this since yesterday, yet i can not solve this question.
Would you mind showing me how to solve it?

Thanks.

The procedure for this type of collision is to write the equations for conservation of energy and momentum
M u = M v + m V
M u^2 = M v^2 + m V^2
Now you can write
M (u - v) = m V
M (u^2 - v^2) = m V^2
Now you can divide equations and continue from there.

 

[tanyareynolds]

Why is the speed of heavy particle unchanged??

 

[kuruman]

I will answer this question with an example even though the thread is almost 8 years old.

A piece of gravel bounces off the windshield of a car. Why is the speed of the car unchanged?

 

[DaveC426913]

This thread is eight years old.

Why is the speed of heavy particle unchanged??

Consider the heavy particle to be an 18-wheeler and the light particle to be you. After a collision between you and an 18-wheeler, how large a change in speed do you intuit the 18-wheeler to experience?

 

[DaveC426913]

All other things being equal, Kuruman's answer is less ... gory.

 

[kuruman]

This thread is eight years old.

Consider the heavy particle to be an 18-wheeler and the light particle to be you. After a collision between you and an 18-wheeler, how large a change in speed do you intuit the 18-wheeler to experience?

Like minds think alike and post alike.