First, if you are submitting an attachment with this...

First, if you are submitting an attachment with this question, then draw free body diagrams for each block. If not, describe the forces acting on each block in sentences: i.e., there is force caused by a hand pushing down on m1 at a 45 degree angle. (Obviously, that statement is made up and untrue - it is just an example.) Second, derive an equation for acceleration of the system in terms of the two masses of the blocks, m1 and m2, the acceleration due to gravity g, and the coefficient of friction ?. Clearly show all the steps of the derivation leading to the final result: the starting point should be, ? F=ma, for each block separately. The answer will require the derivation of three different equations describing this system: one for the orange block and two for the horizontal and vertical directions of the blue block. Third, what should be the minimum mass of the orange block in terms of the other parameters for the system to accelerate?

Transcript

00:01 In this video, i'm going to go over an exercise using a newton's second law.

00:07 And what newton's second law says is that the sum of all forces acting on an object equal that object's mass times its acceleration.

00:17 So what we're going to be looking at is a setup of two blocks.

00:22 One is resting on a table.

00:24 One is attached to it by a thin string that passes over a pulley and hangs off the end of the table.

00:32 So let me draw that for you very quickly.

00:35 So we have a blue block on top of the table.

00:38 Okay.

00:38 And there's some friction between the block and the surface of the table.

00:42 We have that connected to this thin string that passes over a pulley and it's connected to an orange block that is hanging freely.

00:52 Right.

00:52 We originally hold these blocks at rest.

00:55 Then we release them and we want to find the acceleration of each block after the moment of release.

01:01 Okay, so we're going to need to apply newton's second law to each block separately.

01:08 Okay, so let's start with making free body diagrams.

01:12 Okay, so for the blue block, right, in the vertical direction, i have the block's weight.

01:21 That's going to be equal to mg, and that is balanced by the normal force.

01:27 Okay, so the force of the table acting on the block.

01:30 Right we know these two are going to cancel out because we have no motion in the vertical direction right let's look at the horizontal direction okay to the right we have the tension from that string okay and to the left we have the force of friction between the block and the table right and that's all of my forces acting on the blue block okay and again we have no motion in the vertical direction so i'm just looking at my forces in the horizontal direction for the blue block.

02:04 So i can write newton's second law for the blue block and we know that it has two forces, the force of friction and the force of tension and that string.

02:13 And before i write down that equation, it's important to define a coordinate system.

02:19 Okay, so i'm going to call any forces or motion to the left, the negative direction.

02:26 Okay, so that's negative.

02:28 And any forces or motion to the right will be positive.

02:33 Okay.

02:34 So as we come down, that will continue to be the positive direction.

02:38 As we go up, that will be negative.

02:42 Okay, and this will come in handy when we get to the orange block.

02:46 Okay, so with that defined, i can write the sum of the forces for the blue block.

02:50 That equals tension, which acts to the right.

02:56 So that's positive.

02:57 Minus the force of friction that acts to the left, so it's negative.