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In the Figure- shown below, situated two masses on a m[ and m2 frictionless, horizontal surface connected by a light are string: A force of the F is exerted On one...

Question

In the Figure- shown below, situated two masses on a m[ and m2 frictionless, horizontal surface connected by a light are string: A force of the F is exerted On one masses to the right Thc acccleration of the system isa) a = Tlmg 6) a = T(m +m)) c) # = T/(I + m2) d) a = mT.Select one:0O ba

In the Figure- shown below, situated two masses on a m[ and m2 frictionless, horizontal surface connected by a light are string: A force of the F is exerted On one masses to the right Thc acccleration of the system is a) a = Tlmg 6) a = T(m +m)) c) # = T/(I + m2) d) a = mT. Select one: 0O b a



Answers

Two masses $m_{1}$ and $m_{2}$ situated on a frictionless, horizontal surface are connected by a light string. A force $\mathbf{F}$ is exerted on one of the masses to the right (Fig. P5.85). Determine the acceleration of the system and the tension $T$ in the string.

All right. So in this problem we have two blocks. So the 1st 1 has mess one kilogram and the otherwise that two kilograms, we connect this to block the by a stream and the way we pulled them with a force equal 60 10. Okay, so we want to find the attention of forcing inside the stream. Ah, but first we need to look at the acceleration. Mr Books. So acceleration, eh? We'll be able to the 60 meters, which is that which is the force acting on the two blocks. Do you go by the total mass? Right. So one kilograms plants, two kilograms. So this gives you two meters second squid and then come back to the first block. So if Richard a free body diagram in the first block to see that Ah, the net for sound. This is only the attention force in east on the street. Right? So the tea so we can listen in question T d Bye bye. One kilogram able to the acceleration that we found here. He quit two meters second squid. So we can. So, for that I'm sorry we can't sell for the attention force able to notice. Okay,

In this problem to mass bodies are kept on a smooth horizontal surface and they are tired with the help of a light string. So let's say this is the smooth horizontal surface on which two masses are kept and they are connected with the help of a string masses are given in the problem, let us say this was the body, this was the mass block A. And this is must this must block B. And this is must block A. And Masa Block A. That is M. A. Is 10-K. Z. And M B Is 20 K. Z. Now, in first we are applying 600 Newton force in two different cases. So in first case we are going to apply at the block E. So if we apply, uh we have to use this instagram one more time. So let me copy this. So it will save our time. No, the 4th f. is applied on the block a. Of magnitude 600 Newton. And we have to determine what is the 10cent force in this case. So this is the situation. A. Now, first we will draw a free body diagram for both the blocks. So if we draw a free body diagram for mass block B. So there will be a normal reaction on block. Be let us say N. B. And there will be weight of the block B. That is MB into G. That will be acting in downward direction. And there will be tens and force in their strength, which will be acting Which will be acting along the string and away from the object. So here the object is be therefore the direction of 10cent will be in the right direction. Now, if you draw the same thing for our four block A. So what are the forces acting on block? A First one will be the normal reaction that will be acting in a poor direction, and then the weight of the block that will be acting in downward direction. Tencent force will act along the string and away from the object, away from the object. It means that it should be either in left or right, but a string is on left side. Therefore the tencent force will act in left a direction. Now the friction, not the applied force is acting in down in the right direction. Now under the action of this force the entire system will move with same acceleration, so whatever be the acceleration of four Block A. The same acceleration will be for Block B. Let us say the acceleration is A. So what will be the Newton's second law of equation for both the blocks? So if you write the motion of equation for Block B. So what we can write is that net force acting in the direction of acceleration. So here the direction of acceleration is A. And the net force in the direction of acceleration is only tencent force. So 10cent force will be equals two massive blog be into acceleration of blog. So from Newton's second law of what we can write is that net forces equals to mass into exploration here. Net forces. Tencent force. And most of the block is M. B. Into A. It is. See this is equation one. Similarly, if you write equation of motion for the block A. So what we can write is that net force acting in the direction of acceleration is equals to mass into acceleration. So the direction of acceleration is the positive direction. So here forces acting in forward direction, intention is acting in backward direction. So what will be the force or net force? So net force will be yeah minus T. So what we can write F dynasty that is net forces equals to mass of A. Into acceleration of A. So from here we can replace the known quantities. So what we can replace tencent with the help of a question one. So we can write F minus MB into a will be equals two M. A into A. Therefore physicals too, M E into A plus MB into A. We can take a common from the right hand side. So F will be equals two M E plus MB into A. So what will the value of actual reason? So actual reason will be forced divided by some of the masses. That is M. A. Plus MB. Now forces given in the problem which is 600 Newton and masses are 10 KZ and 20 KZ. So the actual reason comes out to be 600 divided by 30 m per second squared, which is 20 m or second describe. So, this is the value of actual reasons. Now we can put the value of actual reason in equation one. So putting equals to 20 yeah meters per second squared an equation one. So what will be the value of tencent? Tencent will be must be. So, what is the must be? It was 20 K Z. Multiplied by actual reason. That is 20 m per second squared. So tense and force becomes 400 newton. So this will be the value of 10cent force in case that is when the forces applied on must block A. Now we have to apply the same must block the same force, but on mass Block B. So in second case we have to use the same diagram, but this time force is applied on mass Block B. All right. So again, we will draw a free body diagram for both the blocks. So, if we go to drop for the Block B, so there will be a normal reaction that the ground will exit on the block. Be. Let us say the forces N. B. And there will be a weight of the block That will be acting in downward direction. So MB in 2G, the force external force will be acting in the left direction, and the Tencent forces acting in the right direction, not for a. The normal force will be acting in a poor direction. Mass or the weight of the block will be acting in downward direction. Tencent horse will be acting in the left direction. Now, let us see that under this, under the action of the external force. The entire system accelerates in left direction with acceleration A. So each block will have the same acceleration A. In the left direction. So what we can write is that both of these are accelerating in the left direction with same axel's recent. Now we can write equation of motion if we write the equation of motion first for block A. So what is the net force acting on the block? A. Net force is in the direction of acceleration. That will be T. That is equals to mass of A. Into X. Terrorism, Let us say this is the equation three. Now, what we can write equation of motion for the block B. So for block B the net force will be so the force F. Is acting in the direction of actual reasons. So F will be positive and tencent forces acting in the opposite direction of actual reason. So we will write minus t. Remember here we are not we are not considering or we are not are dealing with the vertical forces. Why? Because these forces will balance each other. There will be no motion in vertical direction. So N. B. Will be equal to and being too easy. But these values are not required for the calculations. So I'm not going to write those equations. I'm only writing those equations which are going to help us to find the value of acceleration and then to find the value of tension since the tension is acting in horizontal direction and acceleration of the objects are in horizontal direction. Therefore we are only concerned with the horizontal forces and accelerations. Okay so what is the net force acting on the blog? That is F dynasty that will be caused to massive blog. Be into actual reason. Now we can replace the value of tencent tea with the help of equation three. So what we can write F minus M. A. into a should be equals two MB into A. Now we can send this Emma into eight them to the right hand side. So F. We'll B equals two M. A. Into a less. And being to A. So F will be close to if we take common acceleration. So A into M E. Less MB. Now if we divide both sides of the equation with me plus MB. So what will be the acceleration? So it will be F upon M. A. Plus MB. So what is F F. 600? Newton and Emmy As 10 and MBS 20 K. Z. So this is equal to 20 m per second squared. Again, we see that the acceleration remains seem that is 20 m per second described. Now if you put the value of acceleration in equation three, so putting Equals to 20 m/s described in Equation three, What will be the value of 10cent? Tencent will be me, which was 10 and two 20 Newton, so this will become 200 Newton. Therefore, in this case, 10cent forces 200 new dinner. So this is the answer. Fun, Part B of the problem. Okay.

This question covered the concept of Newton's second law, The mass and one of them to pull together by your 4th earth. Therefore we can consider the mass and one of them to has a constant acceleration. Okay, that is a Let's consider the mass M one and M two. This whole other system. Okay, Now, from the Newton's Second Law, we can right uh, f can be the tennis M one plus M two and to eight. The absolution A and Britain is fo born. I am one plus M two also absorbed the values. The acceleration is equivalent to the forces 12 Newtons and the mass and one is three kg And the mass and two is 1 Kg. Therefore the exploration is three m per second square and the correct option is option C.

I had to see the diagram you to consider for the questions. So that is it block having mass is pulled by a rope of mass smaller, right small with the force of Okay, what we can do over here in the first place, I need to say that it is saying. So basically we can clearly see that the small sort of the block robbed by some masses. So it will most people where the gravitational force so we can believe we will be reached at the point when it had obviously don't have 10 20 they have uh you know the side wise point of the block any, the point mass is pulled upwards so that MG balances out uh group attention. So and uh it is something that Tencent have a component in that direction. So it is broke. This rope is sagging. Okay sense. Okay. And find the explanation of the rope and block planned execution of rope and the block. Okay, so uh So the explanation the only 4:15 of the original component. So basically a solution, what if we're taking both of the system? That's a lesson with a mask times of excellence and will be network for the radio six innocent. It will be a phone M plus and right. And the next part calculate is that the force on the block from the rope? Mhm. Force on the block from the very simple, very very simple question. What we can do over here is that course on the block due to road that will be nothing but a mass stamp of excellence and were responsible for the motion of the block. Okay, so this will be my last effort to listen to mass types of excellence and explicitly department F upon employees and and plus a small handful M. F upon and plus them. So this will be the fourth in the next part, the uh the tension in the rope at its midpoint. So 10cent in the room, a robe at the midpoint will be nothing. But at the middle point at the middle point, this Jensen should be responsible for the rest of the motion of the mask. To strengthen T equals nothing but mass. M plus half of the rock mass. Because this is the middle point into a so it will be M plus a small um upon to into F upon and bless them. Okay, thank you.


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