Understanding Algebraic Unknowns in Physics Problems

[ZedCar]

Homework Statement

The unknowns below read as "m sub 1", "rub sub 2" etc.
The maths part of a physics problem states:

r1/v1 = r2/v2

Combining these with equation :

m1r1 = m2r2

gives:

v1/v2 = r1/r2 = m2/m1

Homework Equations

The Attempt at a Solution

Would anyone be able to explain to me how they have gone to the final line of

v1/v2 = r1/r2 = m2/m1

Thank you!

 

[mfb]

You can re-write
r1/v1 = r2/v2 as v1/v2=r1/r2
and
m1r1=m2r2 (I think you mean this) as r1/r2=m2/m1.

 

[HallsofIvy]

Homework Statement

The unknowns below read as "m sub 1", "rub sub 2" etc.
The maths part of a physics problem states:

r1/v1 = r2/v2

This is the same as saying that v1/v2= r1/r2 as you have below.

Combining these with equation :

m1r1/m2r2[/quote]
This is not an equation and does not say anything. What did you mean to say?

gives:

v1/v2 = r1/r2 = m2/m1

If you meant to say "m1r1= m2r2" above, yes, that is correct.

Homework Equations

The Attempt at a Solution

Would anyone be able to explain to me how they have gone to the final line of

v1/v2 = r1/r2 = m2/m1[/quote]
You had, initially, r1/v1 = r2/v2. Multiply both sides by v1/r2 to get (r1/v1)(v1/r2)= (r2/v2)(v1/r2). On the left, the "v1" terms cancel leaving r1/r2. On the right the "r2" terms cancel leaving v1/v2. That is, r1/r2= v1/v2.

If you also have m1r1= m2r2, then dividing both sides by m1r2 gives (m1r1)/(m1r2)= (m2r2)/m1r2). The "m1" terms cancel on the left and the "r2" terms cancel on the right leaving r1/r2= m2/m1. Thus r1/r2= v1/v2= m2/m1.

Thank you!

 

[HallsofIvy]

Homework Statement

The unknowns below read as "m sub 1", "rub sub 2" etc.
The maths part of a physics problem states:

r1/v1 = r2/v2

Combining these with equation :

m1r1/m2r2

This is not an equation. Did you mean "m1r1= m2r2"?

gives:

v1/v2 = r1/r2 = m2/m1

Homework Equations

The Attempt at a Solution

Would anyone be able to explain to me how they have gone to the final line of

v1/v2 = r1/r2 = m2/m1

Thank you!

You have initially, r1/v1 = r2/v2. Multiply both v1/r2. On the left the "v1" terms cancel and you get (r1/v1)(v1/r2)= r1/r2 and on the right the "r2" terms cancel and you get (r2/v2)(v1/r2)= v1/v2 so v1/v2= r1/r2.

If you actually meant m1r1= m2r2, then divide on both sides by m1r2. On the left, (m1r1)/(m1r2), the "m1" terms cancel and you get r1/r2. On the right, (m2r2)/(m1r2), the "r2" term cancel and you get m2/m1: v1/v2= r1/r2= m2/m1.

 

[ZedCar]

This is not an equation. Did you mean "m1r1= m2r2"?

Yes.

Apologies for that. I have now corrected the initial question.

 

[ZedCar]

I understand it now. Thank you.

Sorry for the confusion earlier!