(g) Use your answers from parts (e) and (f) to get an...

(g) Use your answers from parts (e) and (f) to get an expression for the magnitude of the tension T. (Use the following as necessary: m1, m2, and g.) T = (h) Use your answers from parts (e), (f), and (g) to find the magnitude of a, the acceleration of the system. (Use the following as necessary: m1, m2, and g.) a = (i) In what direction will each mass accelerate? mass m1 ---Select--- mass m2 ---Select--- (j) Suppose m1 = 9 kg and m2 = 13 kg. What is the tension in the string? T = (k) Suppose m1 = 9 kg and m2 = 13 kg. What is the value of the acceleration? a = (l) Suppose that m2 starts from rest at a height of 13 m. Use the kinematic equations to determine how long it takes for m2 to hit the ground.

Transcript

00:01 In this problem, we have been given that there are two blocks of masses m1 and m2.

00:06 And these two blocks are connected using a string which passes through a frictionless pulley.

00:14 So this is the designed simple atwood machine.

00:17 And here in this case, we need to figure out the accelerations and the tensions.

00:25 So basically we will be using the equations to get the magnitude of the tension.

00:29 So as we can observe, the free body.

00:31 Diagram there will be the weight of this blocks acting in the downward direction and the tension will be along the string directed away from the mass and let's say m2 is coming down so in that case a will be the acceleration that both the objects will have and as they are connected the accelerations will be same and we apply here the equations of newton's laws of motion that is the net force is equal to mass times the acceleration.

01:02 So considering block one, the net force here will be t minus m1g, because the block is being accelerated in the upward direction.

01:10 So the net force will be its mass times the acceleration.

01:13 So that's equation one.

01:15 And considering the free body diagram of object two, the equation will be m2g minus t.

01:21 That will be m2 times a.

01:23 So here, as we need to figure out, the magnitude of the tension.

01:28 So in that case, we just divide both the equations so that we eliminate a.

01:33 So dividing it, we get t minus m1g divided by m2g minus t is equal to m1 by m2.

01:41 Let's cross multiply it.

01:43 We get m2 times t minus m1m2g is equal to m1m2g minus t times m1.

01:53 And as we need to determine the tension, we take the terms containing t to the left and rearrange change to get the total tension as 2 times m1 m2g divided by m1 plus m2 so that's the magnitude of the tension and in the next case now we have to figure out the magnitude of acceleration so for that we will simply add the two equations 1 and 2 so that the equation becomes m2 minus m1 g is equal to m1 plus m2 times a so from from here we can eliminate and figure out a as m2 minus m1 into g divided by m1 plus m2.

02:37 So that will be the magnitude of acceleration that both these blocks will have.

02:42 And here if we observe the direction in which the masses accelerate, so here we will consider their masses.

02:50 So the given mass is 7 kg for m1 and so it's 7 kg for m1 and and 13 kg for m2...

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