How Does the Formula for Acceleration in a Pulley System Work?

[Yshai24]

Homework Statement

A 230-g air track glider is connected to a string hanging over a frictionless pulley. A 100-g mass hangs from the other end of the string. a) Draw force diagrams for the glider and the hanging mass. b) Find the acceleration of each.

Homework Equations

F=ma
a=m2/(m1+m2) x g

The Attempt at a Solution

So I attempted solve this problem many ways. My textbook was not helping at all so I googled information on pulley systems. I got an example that fit this and I plugged in the numbers and got the answer to b. I don't need help with the free body diagram, just with understanding this.

The equation I found was a= m2/(m1+m2)x g. So I plugged in the values: a=.1kg/(.23kg+.1kg) x g=2.97m/s2

The problem is, I have no clue how that formula works or why it was used. I initially tried to solve the problem by adding the forces and dividing by the total mass, but I was kind of lost.

Any help is greatly appreciated.

 

[Yshai24]

Solved I think

So right after I posted this, I think I solved it:

The two tension forces cancel out and the normal force on the glider and the weight force for the glider cancel out. So the only force remaining is the weight force on the 100g hanging mass right? So then I do:

w=(.1kg)(9.8m/s2)=.98N

a=.98N/.33=2.97m/s2

I tried this earlier but was only using the mass of the glider and not both objects. Though I still don't understand how the other equation in my first post worked?

 

[voko]

At the glider end of the string: $m_1 a = T$. At the mass end of the string: $m_2 a = m_2 g - T$. Note $a$ is the same on both end because the mass and glider move together. Solve for $a$.