Why does the heavier cart get greater velocity than the lighter one?

[VitaminK]

Homework Statement

So I did this lab at school where we had to investigate conservation of momentum. A lighter cart was set in motion (friction free track) towards a heavier stationary cart. After collision the heavier cart got at greater velocity. Why? Are there any energy transformations occuring during the collision?

Relevant Equations

m1×v+m2×v= -(m1×Vo)+m2×Vo

I'm thinking some of the kinetic energy and momentum from the lighter cart transferred to the heavier.

 

[PeroK]

Homework Statement:: So I did this lab at school where we had to investigate conservation of momentum. A lighter cart was set in motion (friction free track) towards a heavier stationary cart. After collision the heavier cart got at greater velocity. Why? Are there any energy transformations occurring during the collision?
Relevant Equations:: m1×v+m2×v= -(m1×Vo)+m2×Vo

I'm thinking some of the kinetic energy and momentum from the lighter cart transferred to the heavier.

Did you expect that the lighter should just bounce off the heavier cart? Is your question how a lighter object can make a heavier one move at all?

 

[VitaminK]

Did you expect that the lighter should just bounce off the heavier cart? Is your question how a lighter object can make a heavier one move at all?

Did you expect that the lighter should just bounce off the heavier cart? Is your question how a lighter object can make a heavier one move at all?

Hi Pero K,
Yes, I expected the lighter to bounce off the heavier cart

 

[PeroK]

Hi Pero K,
Yes, I expected the lighter to bounce off the heavier cart

What if the cart is just a bit lighter? What if it was only $1g$ lighter? And does it matter how fast you fire the lighter cart? What if the lighter cart was moving at $100m/s$?

Do you know how to work with the equations of momentum conservation?

 

[VitaminK]

What if the cart is just a bit lighter? What if it was only $1g$ lighter? And does it matter how fast you fire the lighter cart? What if the lighter cart was moving at $100m/s$?

Do you know how to work with the equations of momentum conservation?

Velocity matter because I get greater kinetic energy. Some of it would transfer to the other cart during collision.
I do know how to work the equation and I am familiar with the law of conservation of momentum.

 

[PeroK]

I do know how to work the equation and I am familiar with the law of conservation of momentum.

Good. Can you post some analysis of the momentum conservation in this case?

 

[VitaminK]

Fair enough but I think my analogy was a good one and he's only focused on the analogy, not on what it means.

I also gave him a strong hint on how to expand his understanding of the situation and there's no follow-up on that either.

Well surprise I'm not a he.

Good. Can you post some analysis of the momentum conservation in this case?

In my case the momentum Before and after collision differ by 0,0002684565kgm/s. Can I in this cases say that the system cannot be considered as isolated

 

[PeroK]

In my case the momentum Before and after collision differ by 0,0002684565kgm/s. Can I in this cases say that the system cannot be considered as isolated

What's your experimental margin of error?

 

[VitaminK]

What's your experimental margin of error?

Haven't calculated that. My teacher wants us to just calculate the before and after momentum and then discuss potential sources of error (high school physics)

 

[PeroK]

Haven't calculated that. My teacher wants us to just calculate the before and after momentum and then discuss potential sources of error (high school physics)

Okay, so that's what you need to do. Analyse potential sources of error.

 

[Cutter Ketch]

It is possible we are misunderstanding your question. You say that after the collision the heavy cart “got a greater velocity”. Many have answered as if you were surprised that the heavier cart had greater velocity than it started with, i.e. zero. That is to say you were surprised the larger cart had any velocity at all. However, from your follow on posts it sounds like you understand that the heavier cart should wind up with some velocity, but perhaps you are surprised by how much velocity.

When you say “greater velocity” what do you mean? Greater than what? What is it about the final velocity of the large cart that surprises you?

If you are saying that it surprises you that the final speed of the heavy cart is greater than the final speed of the lighter cart, then yes, I can see where your intuition might not have expected that, but it is perfectly understandable in terms of the conservation of momentum. The best example of that is the case where the masses are equal. After the collision the incoming cart has no velocity, and the originally stationary cart has all the velocity.

Perhaps part of the reason you are having trouble understanding this is because you wrote your equation wrong. You wrote:

Relevant Equations::
m1×v+m2×v= -(m1×Vo)+m2×Vo

That is incorrect. The idea is that the total momentum of the two carts does not change before and after the collisions. You need to distinguish their individual initial and final velocities:

$m_1 v_{1i }+ m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}$

The initial velocity of the second cart is zero so this becomes

$m_1 v_{1i } = m_1 v_{1f} + m_2 v_{2f}$

The velocities have direction which will come in here as signs.

To go further you need to say something more about the collision. In physics problems they almost always use one of two easy to calculate extremes: A) perfectly elastic implying that energy is conserved or B) perfectly inelastic, implying that the objects stick together and the final velocities are the same.

 

[hutchphd]

The best example of that is the case where the masses are equal. After the collision the incoming cart has no velocity, and the originally stationary cart has all the velocity.

You should include the words "for a purely elastic collision" here I think. And it always surprises me when I see it.