Solving the Mystery of Wrench Work Ratios

In summary, the conversation revolves around the calculation of torque and work done using different wrench lengths to tighten a nut. The length of the wrench is directly proportional to the work done, with a 20 cm wrench requiring twice the force as a 10 cm wrench. The ratio of work done is 0.5, but this is incorrect and the use of the nut's radius is unclear. The final conclusion is that the ratio of work done is 1, as confirmed by both parties involved.
  • #1
Saitama
4,243
93

Homework Statement


(see attachment)

Homework Equations


The Attempt at a Solution


If a force a F acts on the farther end of the wrench, the torque due to it Fl where l is the length of wrench. The work done by this torque for one full turn is Fl*(2##\pi##)
For wrench A, l=10 cm, and for wrench B, l=20cm.
Therefore the ratio of work done is 0.5. But this is wrong. :confused:
I don't understand why they have given the radius of the nut. I haven't used this information and I have no idea about where to use this.

Any help is appreciated. Thanks!
 

Attachments

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  • #2
If a force F is required to tighten the nut using the 10 cm wrench, what force is required with the 20 cm one?
 
  • #3
F/2?
 
  • #4
Pranav-Arora said:
F/2?
Right.
 
  • #5
Doc Al said:
Right.

But what next? Does that mean the ratio is 1?
 
  • #6
Pranav-Arora said:
But what next? Does that mean the ratio is 1?
That's what I would say.
 
  • #7
Doc Al said:
That's what I would say.

Thanks a lot Doc Al! :smile:
 

What is a wrench work ratio?

A wrench work ratio is a measurement of the amount of work that can be done with a wrench compared to the amount of effort put into using it. It is calculated by dividing the output force (the force applied by the wrench) by the input force (the force applied by the user).

Why is it important to solve the mystery of wrench work ratios?

Solving the mystery of wrench work ratios can help us understand the efficiency and effectiveness of using wrenches as tools. It can also help us optimize our use of wrenches and potentially improve their design for more efficient use.

How can wrench work ratios be measured?

Wrench work ratios can be measured by using a dynamometer to measure the output force of the wrench and comparing it to the input force applied by the user. This can be done for different types of wrenches and under different conditions to get a more accurate understanding of their work ratios.

What factors can affect wrench work ratios?

Wrench work ratios can be affected by several factors, including the design and quality of the wrench, the amount of lubrication used, the condition of the fastener being turned, and the strength and technique of the user.

Are there any real-life applications for understanding wrench work ratios?

Yes, understanding wrench work ratios can have real-life applications in industries that heavily rely on wrenches for work, such as automotive repair, construction, and manufacturing. It can also be helpful for DIY enthusiasts and hobbyists who use wrenches frequently.

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