Is Tension Always Equal to Weight in Physics Problems?

[cerberus9]

Homework Statement

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.

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.

 

[CompuChip]

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

What are all the forces acting on the block?

 

[cerberus9]

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.

 

[tiny-tim]

Welcome to PF!

Hi cerberus9! Welcome to PF!

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.

You don't seem to understand the fundamental difference between the left and right and sides of F_total = 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. ​

 

[cerberus9]

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

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

so then do i just add the weight onto that?

oh and thanks for the welcome :)

 

[rock.freak667]

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

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

so then do i just add the weight onto that?

oh and thanks for the welcome :)

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

 

[cerberus9]

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

 

[rock.freak667]

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

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 F_net,T and mg would be

F_net=T-mg => ma_net=T-mg

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

 

[tiny-tim]

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

so then do i just add the weight onto that?

You have to be logical …

You're correct so far, that F_net= 3 …

so the next question is, what is F_net?

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

 

[cerberus9]

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 F_net,T and mg would be

F_net=T-mg => ma_net=T-mg

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

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

oh boy, I'm horribly horribly confused.

 

[cerberus9]

You have to be logical …

You're correct so far, that F_net= 3 …

so the next question is, what is F_net?

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

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?

 

[tiny-tim]

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

Oh, you didn't write that before!

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

(except there's no such thing as a_net … 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? )

 

[cerberus9]

Oh, you didn't write that before!

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

(except there's no such thing as a_net … 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? )

T=63 N right?

 

[tiny-tim]

T=63 N right?

If g = 10, yes.

 

[cerberus9]

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

and yes, g=10

 

[tiny-tim]

physics is equations

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

and yes, g=10

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!

 

[cerberus9]

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!

okayy thanks so much

 

[CompuChip]

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

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?)