Homework Help: Calculate moment of a special wrench

1. Feb 18, 2013

jonjacson

1. The problem statement, all variables and given/known data

The specialty wrench shown in the figure is designed for access to the hold-down bolt on certain automobile distributors. For the configuration shown where the wrench lies in a vertical plane and a horizontal 200-N force is applied at A, perpendicular to the handle, calculate the moment applied to the bolt at O. For what value of the distance d would the z-component of be zero?

2. Relevant equations

M = r x F ;

M= Fd

3. The attempt at a solution

Well I succesfully calculated the moment around O as M=-48.6j -9.49k Nm but I failed to calculate the second part of the problem.

It was asking for d in order to make Mz equal to zero.

Using M=Fd I have:

M=√My2+Mz2 = F d

From that equation I have to find d in order to make Mz zero so I substitute Mz for zero and I calculate te value of d:

√My2=Fd

d=My/F=48.6/200=0.24

But the book gives a value of 74.5 mm, What am I doing wrong?

Thanks!

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Last edited: Feb 18, 2013
2. Feb 18, 2013

voko

You could solve this in two different ways. First, you could express r as a function of d, then use the M = r x F to find the dependence on d.

Or, you could recall that the moment about an axis is proportional to the distance from the axis.

3. Feb 18, 2013

jonjacson

Ohh, I´m sorry, you are right. I was assuming that d was the moment arm but it´s not, in this problem is the distance d as it´s shown in the picture, what a ridiculous mistake.

Now I find the correct answer:

d=70/cos(20)=74,5 mm

Thank you very much!