Is Tension Always Equal to Weight in Physics Problems?

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Homework Help Overview

The discussion revolves around a physics problem involving a 6.00 kg mass being accelerated upwards by a tension in a string. Participants are exploring the relationship between tension and weight in the context of Newton's laws of motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to determine the tension in the string by considering the forces acting on the mass, including weight and tension. Questions arise about the application of Newton's second law and how to account for acceleration in the context of these forces.

Discussion Status

The discussion is active, with participants questioning their understanding of the forces involved and how to construct the correct equations. Some guidance has been provided regarding the relationship between net force, tension, and weight, but multiple interpretations and levels of understanding are evident.

Contextual Notes

Participants are navigating through the implications of upward and downward acceleration on tension and weight, with some confusion about how to apply the equations correctly. There is an acknowledgment of the need to consider limiting cases and the physical meaning behind the results.

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

What are all the forces acting on the block?
 


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:
Welcome to PF!

Hi cerberus9! Welcome to PF! :smile:
cerberus9 said:
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 Ftotal = ma …

all forces go on the left,

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

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

carry on from there. :smile:​
 


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 :)
 


cerberus9 said:
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 :)


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


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


cerberus9 said:
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 Fnet,T and mg would be

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

Do you have a better understanding in how to construct the equation?
 
cerberus9 said:
… 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?

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 … ? :smile:
 
  • #10


rock.freak667 said:
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?

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


tiny-tim said:
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 … ? :smile:

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
cerberus9 said:
Wait, so then for the manet=T-mg, can't you cancel out m on both sides?

Oh, you didn't write that before! :rolleyes:

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 = … ? :smile:

(and yes, you could divide everything by m, but why would you want T/m? :wink:)
 
  • #13


tiny-tim said:
Oh, you didn't write that before! :rolleyes:

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 = … ? :smile:

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


T=63 N right?
 
  • #14
cerberus9 said:
T=63 N right?

If g = 10, yes.
 
  • #15


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

and yes, g=10
 
  • #16
physics is equations

cerberus9 said:
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. :smile:

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


tiny-tim said:
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. :smile:

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 :smile:
 
  • #18


tiny-tim said:
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?)
 

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