the ground. The system is initially held at rest, and is then released. We will learn to calculate the
acceleration of the masses, the velocity of mass m when it moves a distance h, and the work done
by the tension force on mass m as it moves a distance h.
Before we start calculating values for acceleration, velocity, and work, let’s go through the three
steps for problem solving:
- Ask yourself how the system will move: From experience, we know that the heavy
mass, M, will fall, lifting the smaller mass, m. Because the masses are connected, we
know that the velocity of mass m is equal in magnitude to the velocity of mass M, but
opposite in direction. Likewise, the acceleration of mass m is equal in magnitude to the
acceleration of mass M, but opposite in direction. - Choose a coordinate system: Some diagrams on SAT II Physics will provide a
coordinate system for you. If they don’t, choose one that will simplify your calculations.
In this case, let’s follow the standard convention of saying that up is the positive y
direction and down is the negative y direction. - Draw free-body diagrams: We know that this pulley system will accelerate when
released, so we shouldn’t expect the net forces acting on the bodies in the system to be
zero. Your free-body diagram should end up looking something like the figure below.
Note that the tension force, T, on each of the blocks is of the same magnitude. In any
nonstretching rope (the only kind of rope you’ll encounter on SAT II Physics), the tension, as well
as the velocity and acceleration, is the same at every point. Now, after preparing ourselves to
understand the problem, we can begin answering some questions.
- .What is the acceleration of mass M?