- #1

Kermit_the_Phrog

- 22

- 3

- Homework Statement
- As a nut is tightened through an angle θ , the friction between the nut and the threads on the bolt increases. This causes an increasing frictional torque, Tf = γθ as illustrated. The maximum forces, F, you can apply to the wrench gives a maximum torque Tw. What is the total work you do in tightening the nut?

A. Twθ

B. Tw (Tf/y)

C. (Tw^2)/(2y)

D. (Tw^2)/y

- Relevant Equations
- W = T θ

NOTE: THIS IS THE GRAPH PROVIDED

At first I approached this problem attempting to solve for the total work done, using the formula

Wtotal = Wmaxforce - Wfriction

I then subbed into the formula, representing the values of work as their torque value times theta, which gave me a longer algebraic solution that was not one of the multiple choice options listed.

ie,

Wtotal = Twθ - Tfθ

= Twθ - (Yθ)θ

= θ (Tw- yθ)

(this is very clearly wrong)

However, now that I've thought about it, the question is phrased in a specific way. It never really asks for the total work, only for the work that YOU do while tightening the nut :

So would it just be

Wmaxforce = T θ

= Tw θ

and thus option A?

Or is the real solution closer to my first approach?

NOTE: i am not really given the final answer so unfortunately I have no idea which final multiple choice answer is correct ¯\_(ツ)_/¯

Thanks in advance!

Wtotal = Wmaxforce - Wfriction

I then subbed into the formula, representing the values of work as their torque value times theta, which gave me a longer algebraic solution that was not one of the multiple choice options listed.

ie,

Wtotal = Twθ - Tfθ

= Twθ - (Yθ)θ

= θ (Tw- yθ)

(this is very clearly wrong)

However, now that I've thought about it, the question is phrased in a specific way. It never really asks for the total work, only for the work that YOU do while tightening the nut :

So would it just be

Wmaxforce = T θ

= Tw θ

and thus option A?

Or is the real solution closer to my first approach?

NOTE: i am not really given the final answer so unfortunately I have no idea which final multiple choice answer is correct ¯\_(ツ)_/¯

Thanks in advance!