# Tension is equal to weight

1. Aug 24, 2009

### cerberus9

1. The problem statement, all variables and given/known data
A 6.00 kg mass is pulled upwards by a massless string. It is being accelerated upwards at a rate of 0.500 m/s^2. Find the tension in the string.

3. The attempt at a solution

I learned that tension is equal to weight, so I assumed T must = 60.0 N. But the answer key says different, so now I'm lost.

2. Aug 24, 2009

### CompuChip

Re: tension

What do you know about Newtons law. In particular, what does the second one say?

What are all the forces acting on the block?

3. Aug 24, 2009

### cerberus9

Re: tension

the second one is F=ma...

there's its weight acting on it, and the tension of the string acting on it...

does the acceleration act on it too?

i still don't get it.

Last edited: Aug 24, 2009
4. Aug 24, 2009

### tiny-tim

Welcome to PF!

Hi cerberus9! Welcome to PF!
You don't seem to understand the fundamental difference between the left and right and sides of Ftotal = ma …

all forces go on the left,

and the acceleration (there'll only be one of that! ) goes on the right.

ok, so weight is a force, and tension is a force …

carry on from there.

5. Aug 24, 2009

### cerberus9

Re: tension

okay so then the weight puts a force of 60 N on the string already.

and then Fnet=ma
so then Fnet = (6.00 kg)(0.500 m/s2)
and Fnet= 3

so then do i just add the weight onto that?

oh and thanks for the welcome :)

6. Aug 24, 2009

### rock.freak667

Re: tension

well you do but do you know why you must add the weight to Fnet?

7. Aug 24, 2009

### cerberus9

Re: tension

yeah because what I found was only the net force without the weight included. right?

8. Aug 24, 2009

### rock.freak667

Re: tension

No the net force includes the weight.

There are two forces acting, Tension(T) and Weight(mg).Tension acts upwards. It accelerates upwards, so the resultant force is in the direction of the tension. So your equation involving Fnet,T and mg would be

Fnet=T-mg => manet=T-mg

Do you have a better understanding in how to construct the equation?

9. Aug 24, 2009

### tiny-tim

You have to be logical

You're correct so far, that Fnet= 3 …

so the next question is, what is Fnet?

It's the sum of all the forces, so it's … ?

10. Aug 24, 2009

### cerberus9

Re: tension

Wait, so then for the manet=T-mg, can't you cancel out m on both sides?

oh boy, i'm horribly horribly confused.

11. Aug 24, 2009

### cerberus9

Re: tension

so since the weight goes down and the tension goes up, that means that the tension is greater than the weight by 3 N, right?

12. Aug 24, 2009

### tiny-tim

Oh, you didn't write that before!!

Yes, that's it, ma =T-mg.

(except there's no such thing as anet … it's just a … a body can have lots of forces, so it can have a net force, but it only has one acceleration!)

Now, the question asks you for T …

so T = … ?

(and yes, you could divide everything by m, but why would you want T/m? )

13. Aug 24, 2009

### cerberus9

Re: tension

T=63 N right?

14. Aug 24, 2009

### tiny-tim

If g = 10, yes.

15. Aug 24, 2009

### cerberus9

Re: tension

so then if the acceleration was down, would i subtract 3N from 60N(weight)?

and yes, g=10

16. Aug 24, 2009

### tiny-tim

physics is equations

If, despite the tension in the string, the mass was falling (with the same acceleration), then yes, ma = T - mg, so -3 = T - 60, so T = 60 - 3.

If you write it out like that, you can't go wrong …

physics is equations

just write out the correct equation, and stop trying to reason it out!

17. Aug 24, 2009

### cerberus9

Re: physics is equations

okayy thanks so much

18. Aug 25, 2009

### CompuChip

Re: physics is equations

Reasoning is fine... afterwards.
When you think you have written down the correct equation and solved it correctly, then it is often worth to try and explain why your answer is reasonable. For example, if the 6 kg mass is on a rope and is accelerating downwards, but you found a tension greater than the weight of the mass (60N) something is wrong. However, if the tension is just a little smaller than the weight, it looks okay. Ask yourself what would happen in limiting cases (e.g. if the tension is equal to the weight -- what motion would the block have?)