Relationship between distance traveled and momentum

[abpandanguyen]

Homework Statement

Two bodies, A and B, arrive at the base of a frictionless inclined plane with equal momenta of magnitude p. If mass_b = 3mass_a, the ratio of the maximum distance that B travels up the plane to the maximum distance A travels up the plane is...
with choices
A) d_b = d _a
B) d_b = 9d_a
C) d_b = 3d_a
D) d_b = (1/3)d_a
E) d_b = (1/9)d_a

Homework Equations

mv = p
not sure what else

The Attempt at a Solution

Knowing they arrive at the base of this inclined plane with the same momentum, I'm thinking that mass_a is traveling at a faster velocity than mass_b. With this, I am assuming that mass_a is going to travel up the inclined plane farther than mass_b, but I do not really know where to start in terms of finding the actual ratio of the distance traveled between the two masses. Please and thank you for helping >_<

 

[tiny-tim]

Welcome to PF!

Hi abpandanguyen! Welcome to PF!

What principle would you use to find the maximum height, given the initial speed?

 

[abpandanguyen]

Alright, so I'm not exactly sure what the name of the principle is, but I used the equation

(v_f)² = (v_i)² + 2a_s(s_f-s_i)

and plugged in a random but reasonable incline to get an acceleration. With this and other initial velocities I plugged in just for the sake of using numbers to get a better idea of what I was doing, I found that E is the best answer.

The numbers I used were:
mass_a = 2 kg
mass_b = 6 kg
so respectively I gave them initial velocities of 6 m/s and 2 m/s and the incline I used was 5^o and I got d_b = 2.34m vs d_a = 21.07m

Yes? No? D:<

 

[tiny-tim]

You're missing the point of this exercise.

Basically, you're using the equation v² = 2as (or v² = 2gh).

a is the same for both masses, so you don't need to know what a is, nor m.

you can find s₁/s₂ just from v₁/v₂

 

[abpandanguyen]

Okaaay, that makes sense to me now. Thank you very much :D

 

[samsorz]

I guess I still don't see the answer, yet, I think it is Db=1/3Da, can anyone confirm this?

thanks

 

[tiny-tim]

I guess I still don't see the answer, yet, I think it is Db=1/3Da, can anyone confirm this?

thanks

Hi samsorz!

(are you the same person as abpandanguyen?)

Write the equation for D_b, and divide it by the equation for D_a …

what do you get? ​

 

[samsorz]

no, i am not the same person, but probably same class :)

assuming that s1/s2 is the same thing as D1b/D2b, then... since you said the velocity is just the v1/v2, and velocity isn't affected by a change in mass, are they equal then?

 

[abpandanguyen]

no, this is abpandanguyen
I got E as my answer. I am pretty sure that is right, unless I just screwed up my equation somewhere. Thanks again btw Tiny Tim.

 

[tiny-tim]

Welcome to PF!

Hi everyone! Welcome to PF, samsorz!

no, i am not the same person, but probably same class :)

assuming that s1/s2 is the same thing as D1b/D2b, then... since you said the velocity is just the v1/v2, and velocity isn't affected by a change in mass, are they equal then?

Sorry, I'm not following you … they start with different velocities, but with equal momenta …

write the equation for D_b, and divide it by the equation for D_a …

what do you get? ​

 

[samsorz]

ok, see if this is better

Pb= mv m=2, v=6, p = 12
Pa=3mv m=1, v=4, p = 12

6/4, 3/2?, I am getting more and more lost :(

EDIT: V^2=2d?, so 36 and 16?

 

[tiny-tim]

ok, see if this is better

Pb= mv m=2, v=6, p = 12
Pa=3mv m=1, v=4, p = 12

6/4, 3/2?, I am getting more and more lost :(

EDIT: V^2=2d?, so 36 and 16?

Hi samsorz!

(try using the X² and X₂ tags just above the Reply box )

If you wrote proper equations, you wouldn't get into this mess!

Write it all out in full (and show us) …

what is the equation relating p_a and v_a?

what is the equation relating p_b and v_b?

so what is the equation relating v_a and v_b?

what is the equation relating d_a and v_a?

what is the equation relating d_b and v_b?

so what is the equation relating d_a and d_b?

 

[samsorz]

what is the equation relating pa and va? p_a=m_av_a

what is the equation relating pb and vb? p_b=3m_av_b

so what is the equation relating va and vb? p_a/v_a=p_b/3v_b

EDIT: the rest I am having trouble finding

 

[tiny-tim]

so what is the equation relating va and vb? p_a/v_a=p_b/3v_b

No, you haven't finished that part yet …

what is v_a/v_b ?

The next step is the relation between v and d.

You wrote v² = 2d, which is the right idea, but you've left something out.​

 

[samsorz]

so what is the equation relating va and vb? V_a/V_b=[P_a/ma]/[P_b/3ma]

I'm not sure what I am leaving out

 

[tiny-tim]

so what is the equation relating va and vb? V_a/V_b=[P_a/ma]/[P_b/3ma]

I'm not sure what I am leaving out

Well, the question tells you the momenta (P_a and P_b) are equal,

so V_a/V_b=[P_a/ma]/[P_b/3ma = 1/3

Carry on. ​

 

[samsorz]

By carry on do you mean there's more parts? or is that it lol

TY

 

[tiny-tim]

By carry on do you mean there's more parts? or is that it lol

TY

I meant …

what is the equation relating d_a and v_a?

what is the equation relating d_b and v_b?

so what is the equation relating d_a and d_b?

hmm … i think misunderstood when you wrote …

I'm not sure what I am leaving out

you meant in v² = 2d, didn't you?

That was supposed to be one of the standard constant acceleration equations …

so where's the acceleration? ​

 

[samsorz]

a is the same for both masses, so you don't need to know what a is, nor m.

You said that earlier so I thought we neglected it

 

[tiny-tim]

a is the same for both masses, so you don't need to know what a is, nor m.

You said that earlier so I thought we neglected it

Yes, we don't need to know what a is …

but that's no excuse for writing an equation that's wrong!