Wretched Wrenches and Blustering Bolts

[WehrdScience]

So I have asked a few wrench questions and bolt questions, now to tie them together (figuratively). Please excuse my variables if they do not match your own. Do I understand that the Ideal Mechanical Advantage of a wrench is like a wheel and axle system where:

IMA = radius (wrench) / radius (bolt)

...and the Ideal Mechanical Advantage of a bolt is also similar to a wheel and axle, but also a screw too where:

IMA = diameter (bolt) / thread pitch (bolt)

And Torque (Work) of the wrench would be:

T = force * distance => force applied to the wrench in Newtons multiplied by the distance of end of wrench from the bolt (radius in (lets say) meters)

But is there not also Torque (Work) of the bolt? Where:

T = force * distance => force applied to the bolt in Newtons multiplied by the distance of bolt (radius in again, meters (to keep the units the same).

BUT, neglecting friction or lubrication or material specifications, shouldn't the work or torque we put into the wrench EQUAL the work or torque onto the bolt? So that:

F(wrench) * d(wrench) = F(bolt) * d(bolt) ?

Where would the mechanical advantage come into play? It seems there are really two problems here...one for the wrench...and one for the bolt.



1) Bottom line...I would like to see a formula that if I know what FORCE I input onto a wrench of X radius...it will tell me the FORCE and TORQUE of the bolt...


2) Also, is the torque calculated in #1 on the head of the bolt or on the end of the bold pressing into the material behind it or both? Because I need the force or torque or pressure (ANYTHING will do and I can convert it backwards or forwards) of the END of the bolt...



Thank you for helping me...it may seem simple to you, but it has been driving me crazy for weeks! I have every measurement needed to make this happen, but please use convenient numbers to help explain these questions.

Thank you all so much, I really appreciate this forum!

-WehrdScience

 

[Valerie Park]

The Ideal Mechanical Advantage (IMA) of a wrench is calculated by dividing the radius of the wrench by the radius of the bolt. This means that if you apply a certain force to the wrench, it will take a smaller force to turn the bolt. The Ideal Mechanical Advantage of a bolt is calculated by dividing the diameter of the bolt by the thread pitch of the bolt. This means that if you apply a certain force to the bolt, it will take a smaller force to turn the bolt. The torque (work) of the wrench is calculated by multiplying the force applied to the wrench in Newtons by the distance from the end of the wrench to the bolt. The torque (work) of the bolt is calculated by multiplying the force applied to the bolt in Newtons by the radius of the bolt (in meters). The force applied to the wrench must be equal to the force applied to the bolt for the same amount of work/torque to be done on both. This means that the IMA of the wrench and the IMA of the bolt must also be equal. To calculate the force and torque of the bolt given a certain force and radius of the wrench, you can use the following formula: F(bolt) = F(wrench) * (d(bolt)/d(wrench))T(bolt) = F(bolt) * d(bolt)Where F(wrench) is the force applied to the wrench in Newtons, d(wrench) is the distance from the end of the wrench to the bolt in meters, d(bolt) is the radius of the bolt in meters, F(bolt) is the force applied to the bolt in Newtons, and T(bolt) is the torque of the bolt in Newton-meters. The torque of the bolt is calculated on the head of the bolt, not the end of the bolt pressing into the material behind it. The force and torque of the bolt are related since torque is the product of force and distance.