Momentum problem: 2 carts, finding initial speed

[emily081715]

Homework Statement

A 2.0-kg cart collides with a 1.0-kg cart that is initially at rest on a low-friction track. After the collision, the 1.0-kg cart moves to the right at0.50 m/s and the 2.0-kg cart moves to the right at0.30 m/s .If the positive direction is to the right, what was the initial velocity of the 2.0-kg cart?

Homework Equations

i know that it is a momentum problem so i am assuming we will use p=mv

The Attempt at a Solution

i originally tried solving for the initial velocity by setting the equation up like this; m1(v2-v1)= m2(v2-v1). when plugging in all the variables and isolating for V1 of the 2.0kg cart i got 0.05 m/s. that is not the correct answer and i am unsure is i missed steps or am doing the problem completely wrong

 

[Orodruin]

m1(v2-v1)= m2(v2-v1)

Is momentum conserved if this equation is fulfilled? The equation states that both carts get the same change in momentum.

Also, it is not clear what you mean by v1 and v2.

 

[emily081715]

Is momentum conserved if this equation is fulfilled? The equation states that both carts get the same change in momentum.

Also, it is not clear what you mean by v1 and v2.

i mean intial velocity for V1 and finial velocity for V2. truthfully i am very confused how to go about this problem

 

[Orodruin]

i mean intial velocity for V1 and finial velocity for V2. truthfully i am very confused how to go about this problem

Well, you have two objects with velocity before and after so this notation is still ambiguous. I suggest you try to think of what I said in the previous post.

 

[Chestermiller]

What is the final momentum of the two carts?

 

[emily081715]

What is the final momentum of the two carts?

would the final momentum

What is the final momentum of the two carts?

would the final momentum be 1.1? i added the momentum of each cart after the collision

 

[haruspex]

would the final momentum be 1.1? i added the momentum of each cart after the collision

In the units being used, yes. But you should always specify the units.

 

[Chestermiller]

would the final momentum

would the final momentum be 1.1? i added the momentum of each cart after the collision

Okay. Now if V is the initial velocity of the mass that is moving, in terms of V, what is the initial momentum of the combination of two masses?

 

[emily081715]

Okay. Now if V is the initial velocity of the mass that is moving, in terms of V, what is the initial momentum of the combination of two masses?

i'm a little confused by the question. wouldn't the initial momentum have to be 1.1 for the initial since the one cart is at rest? so is the initial then 1.1?

 

[Chestermiller]

i'm a little confused by the question. wouldn't the initial momentum have to be 1.1 for the initial since the one cart is at rest? so is the initial then 1.1?

Okay. Now, what did its velocity have to be for this to be its initial momentum?

 

[emily081715]

Okay. Now, what did its velocity have to be for this to be its initial momentum?

would it need to be 0.55?

 

[emily081715]

actually that's the correct answer, thanks for the help and helping me through

 

[Orodruin]

i'm a little confused by the question. wouldn't the initial momentum have to be 1.1 for the initial since the one cart is at rest? so is the initial then 1.1?

Please use units. The number 1.1 has no meaning as a momentum without a specification of the units used. They could be kg m/s (as they should here), but without specifying we cannot know this and you may as well be referring to solar masses * light years / hour.

Always specify the units!

 

[jedishrfu]

Khan academy has many good videos on physics. Here's a list of the ones related to momentum:

https://www.khanacademy.org/science/physics/linear-momentum

Perhaps after reviewing them the problem will be come easier to solve.

As Orodruin has said earlier, in physics you must pay attention to the units of measure and you must specify them each time you write down a number otherwise that number is meaningless. You can't work with the numbers until the units are common and properly accounted for.

In your case, the preferred units of measure are meter, kilogram and second (MKS system).

The key point of this problem is that momentum is conserved before and after the collision. Hence the total momentum of the objects before the collision must match the total momentum of the same objects after the collision. Also momentum is a vector quantity meaning you must vectorially add it up before and after.