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December 21, 2014

December 21, 2014

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

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 10:17pmIf 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 -
**Hannah**, Thursday, January 17, 2008 at 10:21pmso for the first part... the initial m1v1 is (4kg)(6m/s). the final is what i can't get. is the final 12kg? arent we only concerned with the first mass in that question?

- Physics -
- Physics -
**Damon**, Thursday, January 17, 2008 at 10:47pmIn 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 10:52pmIn 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 10:54pmThat is it, ten before 11, I am turning into a pumpkin ! Or at least I am turning into sleep.

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