Torque: Two pulleys wheels connected by a belt

[Janiceleong26]

Homework Statement

Ok, so first I find the tension on the top portion of the belt..
3.0=T(100/1000) , T-> tension
T=30N , though I'm not sure if taking the diameter of Q is correct.
Then I find the torques on wheel P, which I multiply the tension with the radius (150/2 mm) which I get 4.5 Nm. But the correct answer is D.
Judging by the correct answer, I assume that they used the radius of Q to find tension, not diameter.. But why radius? I thought torque is force multiply perpendicular distance separating the two forces?

 

[Orodruin]

But why radius? I thought torque is force multiply perpendicular distance separating the two forces?

So which are the two forces you are thinking of here? Which forces will be acting on the pulley Q?

In general, you can compute the torque around any point. Some points are just more convenient than others.

 

[Janiceleong26]

So which are the two forces you are thinking of here? Which forces will be acting on the pulley Q?

In general, you can compute the torque around any point. Some points are just more convenient than others.

Tension force of upper part of string on Q and P. Only the tension force of the top portion of the string is acting on pulley Q.

 

[Orodruin]

Only the tension force of the top portion of the string is acting on pulley Q.

If this was true, the pulley would be accelerating.

 

[Janiceleong26]

If this was true, the pulley would be accelerating.

Reaction force of pulley on string? I can't think of any other forces..since frictional force and weight force is negligible..

 

[Orodruin]

Reaction force of pulley on string? I can't think of any other forces..since frictional force and weight force is negligible..

There is one force which you are not thinking about - probably because it does not give any torque around the point around which you are probably computing the torque ...

 

[Janiceleong26]

There is one force which you are not thinking about - probably because it does not give any torque around the point around which you are probably computing the torque ...

The weight of the pulley wheels ?

 

[Orodruin]

A priori, yes. But not what I was thinking about. Do not bother yourself too much, it is irrelevant when computing the torque. I only mention it because you started talking about separating two forces. This is not the definition of a torque. A torque is the force multiplied by the perpendicular distance to the point which you are considering the torque about. This distance is the radius, not the diameter (assuming you are considering the torque around the center of the pulley - otherwise the other forces do matter). You did this correctly for the pulley P where you used the radius. There is nothing different for Q.

 

[Janiceleong26]

A priori, yes. But not what I was thinking about. Do not bother yourself too much, it is irrelevant when computing the torque. I only mention it because you started talking about separating two forces. This is not the definition of a torque. A torque is the force multiplied by the perpendicular distance to the point which you are considering the torque about. This distance is the radius, not the diameter (assuming you are considering the torque around the center of the pulley - otherwise the other forces do matter). You did this correctly for the pulley P where you used the radius. There is nothing different for Q.

Ok, so if the bottom part of the string has tension, the torque would be the tension multiply by the diameter of the pulley, am I right? But since the string is slack at the bottom, we take the radius of the pulley (moments about the centre of the pulley)

 

[Orodruin]

Ok, so if the bottom part of the string has tension, the torque would be the tension multiply by the diameter of the pulley, am I right? But since the string is slack at the bottom, we take the radius of the pulley (moments about the centre of the pulley)

No, if both strings would have tension their torques act in different directions, giving a net torque of zero.

 

[andrevdh]

Where do the 3.0 Nm torque on Q come from?
What is responsible for it.

 

[Janiceleong26]

Where do the 3.0 Nm torque on Q come from?
What is responsible for it.

The tension of the upper part of the string?

 

[Janiceleong26]

No, if both strings would have tension their torques act in different directions, giving a net torque of zero.

Oh right.. What is the difference between torque and moments?

 

[Orodruin]

Oh right.. What is the difference between torque and moments?

A torque is by definition a force moment. A moment is a more general concept.

 

[Janiceleong26]

A torque is by definition a force moment. A moment is a more general concept.

Thanks

 

[andrevdh]

No. Read the question carefully.

 

[Janiceleong26]

No. Read the question carefully.

The rotation of Q by the motor?

 

[andrevdh]

Yes. That is the torque supplied by the motor. It is opposed by the torque of the
tension in the belt. The sum of these torques must be zero. I think that is what
Orodruin was getting at. See if you can set such an equation up. It is very simple.
Not that difficult at all.

 

[Orodruin]

I think that is what
Orodruin was getting at.

Not really, this I took for granted. There is also a force from the axle on the pulley (or the pulley would have a linear acceleration), which is the additional force I was thinking of. It is irrelevant for the problem because you can always solve it taking the torque around the center of the pulley and the moment arm of this force is zero there. The only reason I mentioned it was that the OP started talking about the perpendicular distance between two forces.

 

[Janiceleong26]

Yes. That is the torque supplied by the motor. It is opposed by the torque of the
tension in the belt. The sum of these torques must be zero. I think that is what
Orodruin was getting at. See if you can set such an equation up. It is very simple.
Not that difficult at all.

Ok. Thank you!