4.39 • Two crates, one with mass 4.00 kg and the other with...

4.39 • Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope (Fig. P4.39). A woman wearing golf shoes (for traction) pulls horizontally on the 6.00-kg crate with a force F that gives the crate an acceleration of 2.90 m/s^2. (a) What is the acceleration of the 4.00-kg crate? (b) Draw a free-body diagram for the 4.00-kg crate. Use that diagram and Newton’s second law to find the tension T in the rope that connects the two crates. (c) Draw a free-body diagram for the 6.00-kg crate. What is the direction of the net force on the 6.00-kg crate? Which is larger in magnitude, T or F? (d) Use part (c) and Newton’s second law to calculate the magnitude of F. Figure P4.39

Transcript

00:01 Hi there, so for this problem, we have the situation that is shown in here.

00:05 So we have to create one and two.

00:14 Okay, they are connected, just as is shown in the figure.

00:21 And then we're applying a force to the right, and we have some tension to the left.

00:32 So we have four kilograms in here and six kilograms in here.

00:38 And then with that set, we are told that a woman pulls this crate with a velocity.

00:47 So it pulls this crate with an acceleration of 2 .9 meters per second square.

00:58 Okay.

00:59 So then with that, we are asked the question for part a of this problem.

01:08 What is the acceleration of the four kilograms crate? so we need to find the acceleration of the mass that is four kilograms.

01:20 So then first of all, what we need to do is to consider that we already have the mass of the other crate, which is six, and it's acceleration.

01:31 So we can determine that the net force over the six kilograms mass, it is just, remember, is this mass times eight acceleration, so let's label that as the mass m1, and this is the mass m2, so we can deference shade.

01:49 So this will be for the mass m1 times its acceleration, so let's label that as acceleration one, and the one that we need to find is the acceleration 2.

01:57 So then in this case, that will be 6 kilograms times 8's acceleration, which is 2 .90 meters per second square.

02:05 So let's use our calculator.

02:06 Later.

02:08 So this gave us 15 .6 newtoms.

02:12 Now to find the, this will be the same force that the mass of 4 kilograms experiences.

02:24 So this will be equal to the mass m2 times acceleration 2.

02:28 So since we want to determine its acceleration, we just solve for that.

02:33 And that will be then what we just determined, 15 .6 divided by 4.

02:38 Now let's use our calculator for this.

02:45 And the valley that we determine in here is 3 .9 meters per second square.

02:52 So that will be the acceleration for the mass of 4 kilograms.

02:58 Now for part b of this problem, the question is to draw a free -party diagram for the 4 kilograms crate and use the diagram in newton's second slot to find the tension team.

03:12 Okay, so then in this case, the only force that we are having for the mass and t is the tension t, which will equal to the force f that we are applying to this.

03:28 So let me just draw the situation in here.

03:31 We have all the tension.

03:33 We have its weight downward...

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