Tension Problem

[michellegu2894]

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In the Tension example problem that uses the pulley system in the GS study manual, what equations were equated to each other to find Tension and how were they equated to each other? My study partner and I stayed at Barnes & Nobles and worked on that prob. for at least 40 min. We know that it is basic high school algebra but we just can't seem to retrieve it out of out brains!

GS Manual 2008 edition page 174-175.

[admin]

The equations are:

F = T - m1g = m1a

and

F = T - m2g = -m2a


There are several ways to solve these simultaneous equations.

Option 1: subtract one equation from the other in order to eliminate T (as mentioned in the book)


T - m1g = m1a

-(T - m2g = -m2a)
-------------------
-m1g + m2g = m1a + m2a

now isolate for a by dividing both sides by (m1 + m2)

[pszopa1343]

I'm having trouble solving for the Tension. The book doesn't show the work getting to the equation

T = g(2m1m2)/(m1+m2)

Any help with this one?

Thx.

[DLBMCAT]

Can anyone help and isolate for T?

[jono6411]

Solve for a in the two eq's given by the admin, set them equal to each other, and solve for T.

T=m1a+m1g -> T-m1g=m1a -> T/m1-g=a
T=m2g-m2a -> T-m2g=-m2a -> -(T/m2)+g=a

T/m1-g=-(T/m2)+g -> T(m1+m2)/(m1m2)=2g -> T= 2g(m1m2)/(m1+m2)