Calculating Acceleration in Air Track System

[leo037]

a mass m is suspended on a string and the glider slides over to the right. the system is frictionless and i'm wondering how to find the acceleration of the system with the mass m as 5 gram, and the glider mass as 40gram

 

[nickjer]

Set up a free body diagram for the mass hanging on the string. Then sum the y-forces to 0, since the ball isn't going accelerating up or down. Then sum the x-forces and set it equal to m*a, since the mass is accelerating to the right.