Question

Someone please help!. A student puts two dynamics carts with a speed
bumper between them on a track and presses them
together. The total mass of the carts is 3.0 kg. Once
the student releases them, the carts spring apart and
roll away from each other. One cart has a mass of
2.0 kg and a final velocity of 2.5 m/s [S]. Calculate
the final velocity of the other cart

Answer 1

First, we need to calculate the momentum of the system before the carts roll away from one another. Can you do this?

Answer 2

p = mv
momentum = mass * velocity

Answer 3

yeah, one second

Answer 4

For the moment I did, p=(3.0kg)(-2.5m/s) =-7.5

Answer 5

momentum*

Answer 6

Ok. That's after the carts have pushed away from one another. We'll need that in a moment, though. What's the initial momentum, before they start moving away from each other?

Answer 7

I'm not sure if this is correct, but wouldn't it be 0 since both they were both at rest before they sprung apart?

Answer 8

Exactly! Well done!

So, they start with zero momentum. We know that momentum is conserved, so after they push away, they'll also have zero total momentum.

You've calculated the momentum of one of the carts, already. We can use these facts to find the momentum of the second cart.

Answer 9

That is:
\[0 = P_{cart1}+P{cart2} = -7.5 + P_{cart2}\]
Note, you can make the 7.5 positive by redefining your coordinates, if you wish.
So, what is P cart2?

Answer 10

I hope this is right. Sorry I'm not very confident. p=(2.5)(2)=5?

Answer 11

sorry -5

Answer 12

Nope.

Here's where we are so far:
\[P_{initial} = P_{final}\]Conservation of Momentum
\[P_{initial} = 0\]Therefore,
\[P_{final} = 0\]
\[P_{final} = P_{cart1} + P{cart2}\]
\[P_{cart1} = -7.5 \frac{kg*m}{s}\]
Putting this together:
\[0 = -7.5 + P_{cart2}\]
So:
\[P_{cart2} = 7.5\]

Now, both carts are 3kg together. Cart 1 is 2 kg. What is the mass of Cart 2?

Answer 13

5kg

Answer 14

3 - 2 = ?

Answer 15

sorry 1kg

Answer 16

Yep. So:
\[P_{cart2} = 7.5 = m*v\]
m = 1, so what is v?

Answer 17

7.5m/s

Answer 18

There you go :)

Answer 19

Thank you.

Answer 20

My pleasure