Pulley question EK physics 471

[astronaut135]

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From ExamKrackers Physics #471. This question was posted a few years ago, but I still don't understand the explanation (you can refer to the diagram in this link too): http://forums.studentdoctor.net/showthread.php?t=753099

This is how I worked it out in my head. The mass on the right has a downward force of 10N, so each of the strings pulling up from it has a tension of 5N. Since the tension of the rope must be the same throughout, the tension on the left hand side of the big pulley must also be 5N. But the book's answer is 6N?

MTHeaded's explanation confuses me. Can you really just divide the total force from the masses by the number of strings to get the tension in the rope? The answer wouldn't even be right...20/6=6.66N, not 6N.

Thanks in advance!!

 

[sazerac]

The mass on the right has a downward force of 10N, so each of the strings pulling up from it has a tension of 5N.

No. That would only be true if the blocks didn't move. However the system is not in homeostasis and the blocks will move. One will accelerate up, and the other will accelerate down. Also, they will accelerate at different rates.

Think about the big pulley on top. There is a total downward force on the big pulley of 20N, from the weights.

Think about what is pulling down on the big pulley. The tension in three strings is pulling down. They are all the same string, so the three tensions must be equal.

As for the 6 vs 6.666 discrepancy, you'll have to examine the actual question. It probably asks "which is the closest answer" or something.

 

[HCN4]

Well I struggled with this question too, so I decided to post how I did it. For the weight to the left (W1) (attached with a single string), we know it will accelerate downwards because for a distance D the string moves down, each string moves D/2 for the other weight lifting it up by less amount, therefore, amplifying force. So now that we know that, W1 = T + ma1 and for the other weight, 2T = W2 + ma2. The second weight gets 2T because it is attached by two strings and since the tension throughout the whole thing is constant, we can use the same letter. For acceleration, since the mechanical advantage of this system is 2, then the acceleration of W1 is twice that of W2. So the first equation becomes W1 = T + ma => 10 N = T + a and the second equation becomes 2T = W2 + 2ma => 2T = 10 N + 2a. If we solve the two equations for T but substituting a, we find that T = precisely 6 N.

 

[Teleologist]

There is no image. But just remember that simple machines such as pulleys never change the amount of work you put in.

 

[tshank]

@HCN4 Why did you put 2ma for the equation 2T = W2 + 2ma ??