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A wrench is of length 0.8m, or any number below 1.0m, I am exerting a force of 20 Newtons on the point A (one end of the wrench), on point B there is a bolt (on other end).

If I calculate the Torque acting on the bolt, I use the Formula.

Torque = Force X Distance from the Pivot Point.

Therefore

Torque = 20N X 0.8m Torque = 16Nm

  1. Can anyone help me understand why the Torque acting on the bolt, less than the input force?
  2. Why is there no mechanical advantage? for any value below 1.0
  3. If the distance is above 1.0m, I see the Torque is higher than the input force, why? I understand that's how maths multiplication works; I believed that any lever always has some mechanical advantage?

[! Description: Image of an Allen Wrench having length of 0.8m and a force of 20 N being applied through it on a bolt]1

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    $\begingroup$ This is the kind of question whereby we need you to tell us what kind of understanding you wish to get. What would possibly be considered a satisfactory answer that you would accept? $\endgroup$ Nov 27, 2023 at 9:52
  • $\begingroup$ Because newtons and newton-meters are not the same thing. $\endgroup$
    – Jon Custer
    Nov 27, 2023 at 9:52
  • $\begingroup$ A physical quantity is a number of units. Only if the units are the same they can be compared. $\endgroup$
    – my2cts
    Nov 27, 2023 at 10:07
  • $\begingroup$ @JonCuster Okay , can you help me understand how 20 Newton's is lower / higher than 16 Newton - meters ? If so what would be the conversion ? How much is 16 Newton meter in just Newton's ? Or vice versa $\endgroup$
    – Newbee
    Nov 27, 2023 at 10:46
  • $\begingroup$ The torque generated by a force depends on the lever arm. A longer lever arm turns the same force on the wrench into more torque to turn the bolt. See also ‘cheater bar’ to get more torque. $\endgroup$
    – Jon Custer
    Nov 27, 2023 at 11:26

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You cannot compare force and torque - they are different attributes measured in different units. Trying to compare $20$ Newtons with $16$ Newton-metres is like trying to compare $20$ seconds with $16$ kilograms.

However, you can compare the forces exerted at each end of the wrench. If the bolt has radius of, say, $1$ cm then the force exerted on the bolt is the torque of $16$ Newton-metres divided by $1$ cm, so it $1600$ Newtons. The mechanical advantage of the wrench is then the ratio of these two forces i.e. $1600$ Newtons divided by $20$ Newtons, which is a mechanical advantage of $80$. This is also the ratio of the two lever arms of the wrench i.e. the ratio of $0.8$ metres to $1$ cm.

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