2015 AP Physics 1 free response 1a

Two blocks are connected by a string of negligible mass that passes over a massless pulley that turns with negligible friction. It is shown in the figure above. We see that the mass M2 of block 2 is greater than the mass M1 of block 1. The blocks are released from rest.

So let's just really quick think about what we think is going to happen here. Block two has a larger mass. They’re connected by this string and pulley system here. Well, if it has a larger mass, they are in the same gravitational field. It’s going to have a larger weight, and so the weight pulling down on block two is going to be larger than the weight pulling down on block one.

As a result, you’re going to have block two accelerating downwards. You’re going to have block one accelerating upwards with the same magnitude. So block one is going to accelerate upwards, and so with that just intuition of what we think is going to happen here, let's try to tackle part A of this.

So, they tell us the dots below represent the two blocks. This represents block one; this represents block two. Draw free body diagrams showing and labeling the forces (not components) exerted on each block. Draw the relative lengths of all vectors to reflect the relative magnitudes of all forces.

Alright, so let's think about what are all the forces acting on each of these blocks. Well, for each of these blocks, you’re going to have the force of gravity. You’re going to have the weight of the blocks acting on them. For example, this first block M1, I'll draw it here first. What is the force of gravity going to be? The force of gravity is going to be its mass times the gravitational field.

Now, what is going to be the force of gravity on block two? Well, it's going to be larger than that. So let me just draw it like this. The force of gravity is going to be M2 * G. How did I know it was going to be larger? Well, M2 has a larger mass and we are in the same gravitational field.

Now we’re not done there. We’re not done yet because now we also have the upward pulling force of the tension in the string. We could think about what the magnitude of that is. We know that the tension is going to be pulling upwards on both of the blocks. But let’s think about what its magnitude is going to be.

In order for block one to accelerate upwards, which is our intuition as to what would happen, the tension—the force of the tension—has to be larger. The magnitude of the tension has to be larger than the magnitude of the weight. In order for block two to accelerate downwards, the magnitude of the tension has to be less than the downward force of gravity. The upward force of tension has to be less than the downward force of gravity.

So the magnitude of the tension is going to be in between the magnitudes of these two weights. So let me draw that: the magnitude of the tension is going to be larger than m1g but smaller than m2g. So maybe like that. So that is tension right there.

And whoops, you’re going to have on this side the same magnitude of your tension pulling upwards, but it's now less than the weight, which means that the block is going to accelerate downwards. We know that these two tension vectors have the same magnitude because of the magnitude of the tension throughout this entire string is going to be the same. When you think about tension, this pulling force can be thought about as what’s happening at an atomic or molecular level; these are the bonds pulling on each other at an atomic level throughout the entire string.

And when we look at it on a macro level, we view that as tension, so there you have it. I’ve drawn the forces on them, but I haven’t drawn them in the right place. I need to draw them on this; I need to draw them right over here. Let me draw that.

I can actually draw a little bit more precisely because they gave us these lines. So on block one, I have the weight, so that is m1g. I also have the tension; I'll make that two of these lines tall. So I also have the tension.

Now, on block two, I have the same magnitude of tension, or same magnitude of tension, I should say. It's now also pulling upwards, so tension. And I have its weight, which is going to be larger than the tension, so its weight. I’ll make it three of these lines tall.

So the way I've drawn it, M2 would have to be three times larger than M1, the way I've drawn it. They don’t tell us that, but they tell us that M2 is larger, so this seems to be right. And we just want to get our intuition here. Since our tension, our upward force, is larger than our downward force, you’re going to have a net upward force which is going to accelerate block one up.

And here you’re going to have a net downward force which is going to accelerate block two down, which is in line with our intuition because block two weighs more than block one.