Calculate Force for Torque of 16Nm Using Spanner Length 24cm

[coconut62]

Question:

"A nut is to be tightened to a torque of 16N m. Calculate the force which must be applied to the end of a spanner of length 24cm in order to produce this torque."

This question is so easy, just take the 16 divide by 0.24 and you get the answer.

But something is confusing me. Please see attached image.

Anyone who would explain it to me, I thank you very much.

 

[Simon Bridge]

If your diagram, the spanner handle is 24cm - but that is not what the question says.
I don't understand the comments on your diagram ...

 

[coconut62]

Sorry, I drew it wrongly.

Okay the main confusion is this:
Since a couple has to have two forces acting, then where is the other force, other than the one you apply on the end of the handle?

 

[haruspex]

Since a couple has to have two forces acting, then where is the other force, other than the one you apply on the end of the handle?

The bolt exerts both a torque and a linear force on the nut. These add up to be equivalent to a single force directly opposing the applied force on the other end of the spanner.

 

[Simon Bridge]

You don't actually need a couple to make something turn do you?

But sure - if there were no other forces present, the spanner would not be able to turn the nut - at least, not in the way we want it to. i.e. if the bolt were not fixed in place, and constraining the nut, the applied force would not result in the required torque.

 

[coconut62]

The bolt exerts both a torque and a linear force on the nut.

What linear force? In which direction?

 

[haruspex]

What linear force? In which direction?

The linear force is equal and opposite (parallel) to the applied force, but its line of action is through the centre of the bolt. This reactive force from the bolt combined with the applied force creates a couple. The reactive couple the bolt exerts on the nut is equal and opposite to that couple. (This all assumes nothing is accelerating.)