Iii three blocks on a frictionless horizontal surface are in...

(III) Three blocks on a frictionless horizontal surface are in contact with each other as shown in Fig. 4-54. A force $\vec{F}$ is applied to block A (mass $m_A$). ($a$) Draw a free-body diagram for each block. Determine ($b$) the acceleration of the system (in terms of $m_A, m_B,$and $m_C$ ), ($c$) the net force on each block, and ($d$) the force of contact that each block exerts on its neighbor. (e) If $m_A=m_B=m_C=$10.0 kg and $F=$96.0 N, give numerical answers to ($b$), ($c$), and ($d$). Explain how your answers make sense intuitively.

Transcript

00:01 Let's talk about this question.

00:02 We are given that three blocks on a frictionless horizontal surface are in contact with each other.

00:08 The force is applied on mass a.

00:10 We have to draw the free body diagram of each block.

00:13 So that's one.

00:15 So let's do that.

00:18 Do we have friction? no, we don't have any friction.

00:20 So that's frictionless.

00:21 So that's a good thing to hear.

00:23 Let's talk about block a.

00:25 So for block a, we have the weight of a.

00:30 The reaction force of a due to the floor and we have this force which is acting on a and there would be a reaction force let's call it r1 between block a and block b so this is for block a likewise if we draw for block b we definitely have a weight of b we have a reaction of uh we have actually the reaction force the upward reaction force is definitely going to be same for all but okay, let's draw it as if b.

01:03 So at b, b has two contact surfaces, each of this.

01:09 So a will exert a reaction force on b, which is r1 over here, and c will exert on b, which is r2, let's say, over here.

01:21 Likewise, we have it for c, wherein we have wc, we have the reaction force c, and we have just one force because b will exert on.

01:31 Which is r2 so r2 will act over here so these are the free body diagrams of all the three blocks the next part talks about let's see the acceleration of the system in terms of mab and mc so this is pretty much easy because the f net is equal to mass which is the net mass so m a plus m b plus mc times acceleration because we are taking this complete system as a unit so that can be assumed as a a block which has a force acting with f and the mass having m a plus mb plus mc this is can be assumed like it so the new mass for the system is m a plus m b plus mc which means that the acceleration is going to be force over m a plus mc so this would be the required acceleration next it talks about the net force which is is acting on each block.

02:37 The net force which is acting on each block.

02:42 Okay...

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