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Tension question

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cashmoney805

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Hey guys, I have a specific question about tension that is really driving me crazy. It may be a little more than I need to know for the MCAT, but whatever. Anyway, here's the question:

A bucket weighing 3.2 kg is hanging from a massless rope. If the bucket is pulled upward by the rope with an acceleration of 1.6 m/s^2, calculate the tension in the rope. So I'm pretty sure there are 2 forces acting on the bucket: mg down, and Ft, tension of the rope, up. So the sum of the forces must = ma. So, Ft - mg = ma. Here's where I get messed up. Since the acceleration is up, don't g and a have to be opposite signs? If I make them opposite signs, i get something like 26.24. However, the answer in my book is 36, which you would get if a and g had the same sign. Can anyone explain why they have the same sign? Thanks so much
 

xanthomondo

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Hey guys, I have a specific question about tension that is really driving me crazy. It may be a little more than I need to know for the MCAT, but whatever. Anyway, here's the question:

A bucket weighing 3.2 kg is hanging from a massless rope. If the bucket is pulled upward by the rope with an acceleration of 1.6 m/s^2, calculate the tension in the rope. So I'm pretty sure there are 2 forces acting on the bucket: mg down, and Ft, tension of the rope, up. So the sum of the forces must = ma. So, Ft - mg = ma. Here's where I get messed up. Since the acceleration is up, don't g and a have to be opposite signs? If I make them opposite signs, i get something like 26.24. However, the answer in my book is 36, which you would get if a and g had the same sign. Can anyone explain why they have the same sign? Thanks so much

You're already taking into account g being negative in your equation, the fact that it's -mg shows that mg is going opposite of a. Remember it's the SUM of the forces = ma, so any negative signs show opposite direction

F = ma
T-mg = ma
T- 3.2(9.8) = 3.2(1.6)
T- 31.36 = 5.12
T = 36.48
 

Vihsadas

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Good exp. Also, this question is definitely not out of the scope for the MCAT. Something similar could show up!

It's important to remember why the equations look the way they do. Just remember that when you're dealing with forces, no matter whether its tension, friction, Normal force, whatever, you have to vector sum the forces to get the right answer.

So when you get these problems in the future, instead of thinking "what formula do I use?", just remember that you need to sum all of the forces at work. If you do it that way then you can't get mixed up in the signs. :)
 

MBHockey

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It also helps to just look at it logically.

You are pulling on a rope (holding a mass) hard enough such that it is accelerating opposite the direction of gravity. Intuitively, this should tell you that you must be pulling harder than the object weighs. Therefore, tension can't be less than the object weighs...you wouldn't be able to pull it up!

Alternatively, you can use a strictly mechanical approach and sketch a free body diagram of the bucket. One arrow from its center pointing down (force of mg; it gets a negative sign) one arrow pointing up from its center (T; it gets a positive sign) and then just sum the forces in the Y direction and set equal to ma (from newton's second law)

This yields:

T - mg = ma

or

T = mg + ma
 

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