Finding the Unknown Penguin Mass: Solving Equations with Multiple Variables

[Gold3nlily]

Homework Statement

The figure here shows four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are m1 = 13 kg, m3 = 17 kg, m4 = 22 kg, T2 = 112 N, and T4 = 224 N. Find the penguin mass m2 that is not given.

Homework Equations

F=ma
a=F/m
(T2/m1+m2) = (T4/m1 + m2 +m3+m4)

The Attempt at a Solution

I understand the concepts of this problem, I know i have to set these two equations equal to one another becasue all of the penguins experience the same acceleration.
(T2/m1+m2) = (T4/m1 + m2 +m3+m4)
I am trying to simplify this equation so that it is set equal to m2 but I have NO IDEA how to get the m2 OUT of the denominator of these fractions! Help please.

 

[Mark44]

What figure?

Also, use parentheses appropriately. You have used some in the 3rd line of your relevant equations and in your solution attempt, but they don't add any clarity whatsoever. The expressions would mean the same with or without the parentheses you added.

I suspect that the m1 and m2 on the left side of your first equation are in the denominator, and that the four masses are in the denominator on the right side.

Here is that equation again with parentheses in the right places.
T2/(m1+m2) = T4/(m1 + m2 +m3+m4)

If a numerator or denominator of a fraction two or more terms, put a pair of parentheses around the entire numerator or denominator.

 

[Gold3nlily]

What figure?

If a numerator or denominator of a fraction two or more terms, put a pair of parentheses around the entire numerator or denominator.

Okay, thank you Mark44.

Here's a link to the pick:
http://edugen.wiley.com/edugen/courses/crs4957/art/qb/qu/c05/fig_5_D.gif

So, T2/(m1 + m2) = T4/(m1 + m2 + m3 + m4) How do I get the m2 out?

1/(m1 + m2) = (T4/T2) x 1/(m1 + m2 + m3 + m4)
Is writing the equation this way any more useful? I don't know what to do next. I tried plugging in the numbers and simplifying but it didn't work. I ended up with m2 + 26 = m2 +13. The m2's cancel out when i do it that way and the equation doesn't make sense. What should I do?

 

[Mark44]

No, that's no help.
Cross multiply, which is equivalent to multiplying both sides by (m1 + m2)(m1 + m2 + m3 + m4)

After you do that, expand (i.e., multiply) the two factors on each side. Then move all the terms that involve m2 to the left side, and move all the other terms to the right side. You should have T2*m2 - T4 * m2 on the left side, or m2(T2 - T4).

Finally, divide both sides by T2 - T4, and you will have solved for m2.

I know i have to set these two equations equal to one another

You never set equations equal to each other: you set expressions equal to each other.

 

[Gold3nlily]

No, that's no help.
Cross multiply, which is equivalent to multiplying both sides by (m1 + m2)(m1 + m2 + m3 + m4)

After you do that, expand (i.e., multiply) the two factors on each side. Then move all the terms that involve m2 to the left side, and move all the other terms to the right side. You should have T2*m2 - T4 * m2 on the left side, or m2(T2 - T4).

Finally, divide both sides by T2 - T4, and you will have solved for m2.

You never set equations equal to each other: you set expressions equal to each other.

I cannot thank you enough! It has been years since I have done this sort of math. I really appreciate your help! I will also try to be more careful with my terminology (equation/expression). Thank you, Thank you Mark44. :)

 

[Mark44]

You're very welcome! I'm glad to have been able to help.