Tension Problem

[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)