Newtonian Mechanics: simultaneous equations

[Medtner]

Homework Statement

Figure 5-12 shows a block S (the sliding block) with mass
M 3.3 kg. The block is free to move along a horizontal
frictionless surface and connected, by a cord that wraps over
a frictionless pulley, to a second block H (the hanging
block), with mass m 2.1 kg. The cord and pulley have neg-
ligible masses compared to the blocks (they are “massless”).
The hanging block H falls as the sliding block S accelerates
to the right. Find (a) the acceleration of block S, (b) the ac-
celeration of block H, and (c) the tension in the cord.

Homework Equations

Block S:
Tx=ma (on the X axis)

Block H:

T-mg=-ma (y axis)

The Attempt at a Solution

I understand the theory and question, my problem lies with my math skills. Because of the two unknown variables you can solve them simultaneously, however the sample problem assumes I remember how to do it!

I want to understand how you can mathematically go from the two equations on top to a=(m/M+m)g on the y axis.
Thank you for the help!

 

[billy_joule]

To avoid confusion you need to use M and m in your relevant equations.
Also note that what you've called Tx is equal to what you've called T (and of course a is the same also) so you can plug one equation into the other and solve for a.

 

[Medtner]

After playing around with the equations I got it. Thanks for the help! I should pay more attention to the variables. :D

I ended up going like:
T-mg=-ma -----> T=-ma+mg
T=Ma -----> (plug in eqquation number 1) -ma+mg=Ma ----->Ma+ma=mg------->a(M+m)=mg----->a=mg/M+m

Would this set up be okay?

 

[billy_joule]

That looks right. Good work.