# What's the inertia of cart A?

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1. Sep 25, 2016

### emily081715

1. The problem statement, all variables and given/known data
A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time as shown graph below:
What is the inertia of cart A?

2. Relevant equations
i am unsure how to even solve for inertia but i know the equation is i=mr^2 except i have never used this equation
3. The attempt at a solution
i tried randomly rearranging formula i know how to use for momentum and got 1.6 kg but i have never solve a problem like this and i'm very confused on how to actually solve for inertia

2. Sep 25, 2016

### Simon Bridge

That is the equation for the moment of inertia I of a body, so you can tell something about it's rotational dynamics. When "inertia" is used by itself it usually means "mass"... look up "law of inertia".

I notice you got it right for your other problem.

3. Sep 26, 2016

### emily081715

Am I just using the equation F=ma? that is what i got when i looked it up. if thats the case i don't know acceleration or the mass of cart A or the F and have three unknown variables

4. Sep 26, 2016

### PeroK

Does Newton's third law tell you anything about the forces involved?

5. Sep 26, 2016

### emily081715

newtons third law says that for action there is an equal and opposite reaction. would this mean the the force acting on the standard cart is equal to the one on cart A?

6. Sep 26, 2016

### PeroK

You need to be more precise. The force that the standard cart exerts on cart A is equal and opposite to the force that cart A exers on the standard cart.

But, do you think there are other forces involved? Hint: how long does the collision last?

7. Sep 26, 2016

### emily081715

i don't think there is any other forces acting on the object. the collision is very quick and doesn't even last a second

8. Sep 26, 2016

### PeroK

That's not right. Normally these problems involve an instantaneous collision. But not in this case. The collision clearly lasts a significant length of time. In fact, it's exactly one second.

9. Sep 26, 2016

### emily081715

so what does that mean?

10. Sep 26, 2016

### PeroK

Do you think friction took a break while the carts got on with their collision?

11. Sep 26, 2016

### emily081715

No, so that means both carts have a force of friction acting on them. i am still unsure how to actually go about solving the question though

12. Sep 26, 2016

### PeroK

Well, this problem is not so easy. To solve this problem, I think you need to really understand what is going on. Then, you need to organise your thoughts. Hit the problem with exactly the right equations and, finally, solve those equations.

The crux of this problem is the relationship between forces and change in momentum. I'm not convinced you understand this well enough yet.

The problem would be much easier with an instantaneous collision. As it stands, I think this question might be a bit hard!

The other question I'm helping you with is really much easier than this one.

13. Sep 26, 2016

### emily081715

both questions need to be answered though, can you keep working on this with me as well

14. Sep 26, 2016

### PeroK

See if you do it without friction first. Ignore friction.

I'll give you one hint. You got $1.6kg$ for cart A. But, that means there is more momentum after the collison than before. So, that can't be right.

15. Sep 26, 2016

### emily081715

i got 0.65kg

16. Sep 26, 2016

### PeroK

From the graph you should be able to see that the mass of cart A is significantly greater than that of the standard cart. This shows the gap between your knowledge of the subject and the knowledge required to solve a problem like this.

17. Sep 26, 2016

### emily081715

can you break down the steps on what i should do to find the answer

18. Sep 26, 2016

### emily081715

should there be less momentum after the collision?

19. Sep 26, 2016

### emily081715

• Poster has been warned not to post multiple threads on the same question...
1. The problem statement, all variables and given/known data
A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time

2. Relevant equations
the law of inertia
F=ma
P=mv

3. The attempt at a solution
i know that inertia in this case means mass, but i am unsure how to solve for it. i tried and got 1.6kg but that cant be right because the momentums before is less then the momentum after the collision. can someone break down the steps that should be taken to solve this question

Last edited by a moderator: May 8, 2017
20. Sep 26, 2016

### Staff: Mentor

What does the question ask for? That seems to be missing from your problem statement.

And what quantity is conserved in elastic collisions like this? How can you use this to solve the problem.

Last edited by a moderator: May 8, 2017