Magnitude of the change in momentum equation

[emily081715]

Homework Statement

A single gas molecule of inertia m is trapped in a box and travels back and forth with constant speed v between opposite walls A and B a distance l apart. At each collision with a wall, the molecule reverses direction without changing speed.
Write algebraic expressions for the magnitude of the change in momentum of the molecule as it collides with wall B.

Homework Equations

Δp

The Attempt at a Solution

i know i am looking for a change in momentum and tried answers such as p=mv. I know the the equation does not depend on l but i am unsure how you are suppose to figure out the answer

 

[Simon Bridge]

The change in something is the final thing minus the initial thing.
For all these momentum problems the start is the same:
1. write a heading "before"
1.1 draw a picture of the initial situation (here it is a particle headed to a wall, it has an arrow on it labelled "v" pointing towards the wall and the particle itself is labelled "m"
1.2 write $p_i=\cdots$ whatever the total initial momentum is ... in this case $p_i=mv$
2. write the heading "after"
2.1 as 1.1 but for the situation "after" the collision ... here the arrow points the opposite way but all the labels are the same: do you see why?
2.2 write $p_f=\cdots$ whatever the final momentum comes to in terms of m and v etc ... remember that velocity is a vector.
3. write the heading "change in momentum $\Delta p = p_f-p_i$
3.1 use the previous 2 sections to do the math.

You seem to be having a lot of trouble with this section of your work because you do not know what many of the terms mean. You should review your coursework so far, paying particular attention to definitions.

 

[emily081715]

The change in something is the final thing minus the initial thing.
For all these momentum problems the start is the same:
1. write a heading "before"
1.1 draw a picture of the initial situation (here it is a particle headed to a wall, it has an arrow on it labelled "v" pointing towards the wall and the particle itself is labelled "m"
1.2 write $p_i=\cdots$ whatever the total initial momentum is ... in this case $p_i=mv$
2. write the heading "after"
2.1 as 1.1 but for the situation "after" the collision ... here the arrow points the opposite way but all the labels are the same: do you see why?
2.2 write $p_f=\cdots$ whatever the final momentum comes to in terms of m and v etc ... remember that velocity is a vector.
3. write the heading "change in momentum $\Delta p = p_f-p_i$
3.1 use the previous 2 sections to do the math.

You seem to be having a lot of trouble with this section of your work because you do not know what many of the terms mean. You should review your coursework so far, paying particular attention to definitions.

would that mean the the equation Δp=-mv-mv?

 

[PeroK]

would that mean the the equation Δp=-mv-mv?

Yes, although since the collision take place at both end sof the box, I'd say you are looking for the maginitude of the change in momentum.

 

[emily081715]

Yes, although since the collision stake place at both end sof the box, I'd say you are looking for the maginitude of the change in momentum.

so i will be using the equation p=mv?

 

[PeroK]

so i will be using the equation p=mv?

You can always use that equation. It's how you interpret it. Do you understand what is happening to the momentum of the ball?

 

[emily081715]

You can always use that equation. It's how you interpret it. Do you understand what is happening to the momentum of the ball?

i understand that before the collision its momentum is p=mv and after the collision, the momentum is the same only it is in the opposite direction so the equation after is p=-mv

 

[PeroK]

i understand that before the collision its momentum is p=mv and after the collision, the momentum is the same only it is in the opposite direction so the equation after is p=-mv

You're right, but if you use an equation twice, you need to distinguish between, in this case, the two momenta. You should be writing:

$p_i = mv$ and $p_f = -mv$

 

[emily081715]

You're right, but if you use an equation twice, you need to distinguish between, in this case, the two momenta. You should be writing:

$p_i = mv$ and $p_f = -mv$

would the mean that the expression i am looking for be mv=-mv

 

[PeroK]

would the mean that the expression i am looking for be mv=-mv

Let's go back to post #3, where you nearly had the answer:

would that mean the the equation Δp=-mv-mv?

I don't really understand why you didn't continue and write: $\Delta p = -mv - mv = -2mv$

Then, you just need to read the question and see that it wants the magnitude of the change in momentum.

 

[emily081715]

Let's go back to post #3, where you nearly had the answer:
I don't really understand why you didn't continue and write: $\Delta p = -mv - mv = -2mv$

Then, you just need to read the question and see that it wants the magnitude of the change in momentum.

is this the equation for the change in momentum of the whole system or when it collides with both walls?

 

[PeroK]

If $\Delta p = -2mv$ what is the magnitude of $\Delta p$?

 

[emily081715]

If $\Delta p = -2mv$ what is the magnitude of $\Delta p$?

2mv

 

[PeroK]

2mv

And that's your answer!