While in class we used those really big machines that were similar to air hockey tables but angled and each had a metal cart that would slide across it. The air between the two metal objects eliminated friction from our equations making it a lot simpler to find the tension. In this lab, we had also had pulleys that change the direction of the force! So by adding and taking away mass from both the cart and pulley's end, we could determine the force and create free body diagrams for this situation. We did a lot of practice problems with the same pulley direction such as those examples from problems we've gone over below.
By using what we've been given, we put the equation Fnet=ma to use! We can use this equation to find the tension of the object pulling. If you think about it, it is the whole setup that is accelerating! Some free body diagrams are shown above. By multiplying the mass of one of the objects and dividing it by the mass of both objects added together, you can find the acceleration, once you've done that you can use Fnet=ma again and solve for tension by either multiplying the mass of a times the acceleration (which I think is the quickest way) or multiplying the mass of object b and gravity (9.8m/s) minus the tension and equalling the mass of object b times the acceleration. There are three steps to this process, it is first drawing the FBD of the system and there are two since there are two objects relying on the pulley, then find the acceleration of the system, and lastly solving for T using one object at a time. You can check your answer by solving using both equations if you want to. :]
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