Posted by **Hannah** on Thursday, January 17, 2008 at 10:07pm.

A 4-kilogram mass has a speed of 6 m/s on a horizontal frictionless surface. The mass collides head-on and elastically with an identical 4-kilogram mass initially at rest. The second 4-kilogram mass then collides head-on and sticks to a third 4-kilogram mass initially at rest.

The final speed of the first 4-kilogram mass is...

The final speed of the two 4-kilogram masses that stick together is...

- Physics -
**Damon**, Thursday, January 17, 2008 at 10:17pm
If they collide elastically the sum of 1/2 m v^2 after has to equal the sum of 1/2 m v^2 s before and the momentums (m1v1+m2v2) must be the same before and after.

This can only happen if the first one stops and the second one proceeds at 6 m/s.

I will leave you to prove that to yourself using those energy and momentum equalities.

Now the second part.

We have no energy conservation now because it is not elastic.

momentum is still conserved though and the two stick so they become one 8 kg mass after

so

4 (6) + 4(0) = 8 (v final)

- Physics -
**Damon**, Thursday, January 17, 2008 at 10:47pm
In the first part of the problem

a 4 kg mass moving at 6 m/s hits another 4 kg mass

that means

4 kg * 6 m/s + 4 kg* 0 m/s = initial momentum

the final momentum is

4 kg * v1 + 4 kg*v2

so

24 + 0 = 4v1 + 4 v2

or

v1 = 6 - v2

then energy

initial ke = (1/2) m v^2 = 2*36 = 72 Joules

final ke is also 72 joules

so

72 = 2 v1^2 + 2 v2^2

36 = (6-v2)^2 + v2^2

36 = 36 - 12 v2 + 2 v2^2

v2^2 - 6 v2 = 0

v2(v2-6) = 0

so v2 = 0 or v2 = 6

v2 may not equal zero unless mass 1 goes straight through mass 2

so

v2 = 6

(like I tried to tell you :) The first one stops and the second one takes over at the original speed.

- Physics -
**Damon**, Thursday, January 17, 2008 at 10:52pm
In the second part of the problem, the 4 kg mass suddenly doubles in mass, so it has to go half as fast to have the same momentum

- Physics -
**Damon**, Thursday, January 17, 2008 at 10:54pm
That is it, ten before 11, I am turning into a pumpkin ! Or at least I am turning into sleep.

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