Pulley question (mechanical advantage)

[heylollipop]

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Sorry guys I don't know how to rotate the picture in this textbox. I thought that the mechanical advantage is 2, since there are 2 supporting ropes in the pulley system.

2 = [(2kg)(10m/s2)] / T
T = 10 N

But answer is B. Someone please help me explain this. Thanks!

(Am I allowed to post a picture of the question like this? If not, please let me know...so I know not to do it in the future)

 

[icedragon]

This is a little tough to visualize conceptually, but I'll do my best to explain it.

Imagine just the lower mass for a second, it will drop at twice the speed as the second pulley by just the way it's drawn out. Likewise the second mass would fall at half the rate as the other string if the other mass wasn't there.

Looking at the lower mass again. It's overall force would be ma = -T + mg. Because the tension and mass are opposing each other and it's dropping downwards. The higher mass should be -1/2(ma) = -2T + mg. Since the lower mass is dropping, then this one is raising upwards at half the rate, but also it has two tensions instead of one holding it up.

Now it's simply plugging each equation into each other. a = (-T + mg)/m
-(1/2)m((-T+mg)/m) = -2T + mg
3mg = 5T
T = 3/5 (10) = 6N

I wouldn't worry too much about this problem, as there are a lot of calculations, but as long as you get the concept you should be fine.

 

[heylollipop]

This is a little tough to visualize conceptually, but I'll do my best to explain it.

Imagine just the lower mass for a second, it will drop at twice the speed as the second pulley by just the way it's drawn out. Likewise the second mass would fall at half the rate as the other string if the other mass wasn't there.

Looking at the lower mass again. It's overall force would be ma = -T + mg. Because the tension and mass are opposing each other and it's dropping downwards. The higher mass should be -1/2(ma) = -2T + mg. Since the lower mass is dropping, then this one is raising upwards at half the rate, but also it has two tensions instead of one holding it up.

Now it's simply plugging each equation into each other. a = (-T + mg)/m
-(1/2)m((-T+mg)/m) = -2T + mg
3mg = 5T
T = 3/5 (10) = 6N

I wouldn't worry too much about this problem, as there are a lot of calculations, but as long as you get the concept you should be fine.

Thanks for the explanation! Why would the lower mass drop at twice the speed as the higher mass?

 

[Blueprint MCAT Tutor]

Thanks for the explanation! Why would the lower mass drop at twice the speed as the higher mass?

You mean you don't know that classic physics concept, "The Law of Conservation of Rope?" 😛

In a given time t, let's say the upper mass rises by 5 cm. That means both of the bits of rope attached to the higher mass are both now 5 cm shorter.

So that's 10cm worth of rope and it has to go somewhere. It's going to roll over the top pulley and the lower mass will drop by 10 cm.