Understanding Algebraic Unknowns in Physics Problems

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In summary, the unknowns are: -m sub 1-rub sub 2-v1-v2-r1-r2-m1-m2The maths part of the physics problem states:r1/v1 = r2/v2Combining these with equation :m1r1 = m2r2gives:v1/v2 = r1/r2 = m2/m1
  • #1
ZedCar
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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!
 
Last edited:
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  • #2
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.
 
  • #3
ZedCar said:

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!
 
  • #4
ZedCar said:

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.
 
  • #5
HallsofIvy said:
This is not an equation. Did you mean "m1r1= m2r2"?

Yes.

Apologies for that. I have now corrected the initial question.
 
  • #6
I understand it now. Thank you.

Sorry for the confusion earlier!
 

Related to Understanding Algebraic Unknowns in Physics Problems

1. What is an algebraic unknowns problem?

An algebraic unknowns problem is a mathematical problem that involves finding the value of unknown variables in an equation using algebraic methods. These problems typically include one or more equations with one or more unknown variables, and the goal is to solve for the values of those unknowns.

2. How do I solve an algebraic unknowns problem?

To solve an algebraic unknowns problem, you can use algebraic techniques such as simplifying, factoring, and substitution. Start by isolating one of the unknown variables in one of the equations, then use that value to substitute into the other equations until you have solved for all of the unknowns.

3. What are the most common types of algebraic unknowns problems?

The most common types of algebraic unknowns problems include linear equations with one or two variables, systems of equations with two or three variables, and quadratic equations with one variable. These types of problems can be solved using different algebraic techniques and may have multiple solutions or no solution at all.

4. How can I check if I have solved an algebraic unknowns problem correctly?

You can check your solution to an algebraic unknowns problem by plugging the values you found for the unknowns back into the original equations. If the equations are satisfied, then your solution is correct. You can also use a graphing calculator to graph the equations and see if the lines intersect at the values you found for the unknowns.

5. Are there any strategies for solving difficult algebraic unknowns problems?

Yes, there are several strategies that can help you solve difficult algebraic unknowns problems. These include using a systematic approach, breaking the problem into smaller steps, and trying different algebraic techniques if one approach does not work. It can also be helpful to practice solving various types of problems to improve your problem-solving skills.

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