Moment about a point of a hammer

[Robb]

Homework Statement

In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of 590 lb⋅in about point A.(Figure 1)

Determine the required magnitude of force F.

Homework Equations

The Attempt at a Solution

M=590lb*in

-590= -Fcos(30)(18)-Fsin(30)(5)

I'm not sure how to deal with F. I know it's simple if given the force to determine the moment but I'm a bit stumped trying to go the other way.

 

[haruspex]

590lb*in

-590= -Fcos(30)(18)-Fsin(30)(5)

I'm not sure how to deal with F. I know it's simple if given the force to determine the moment but I'm a bit stumped trying to go the other way.

How would you solve 3=x+2x?

 

[Robb]

So, F=72.9431?

 

[haruspex]

So, F=72.9431?

Not what I get. Please post your working.

 

[andrewkirk]

Let $X$ be the point where the force is applied to the handle.

The angle you need to use is not 30 degrees but the angle $\alpha$ between the force vector and the perpendicular to the line segment $\overline{XA}$. You can calculate that angle using geometry, from the information given.

The Torque (moment) will be the force multiplied by $\cos\alpha$ and the length of $\overline{XA}$.

By the way, that's one weird hammer! Based on the drawing and the dimensions given, the claw is about eight inches long! That's a gemmy, not a hammer. The drawing is not to scale. The 18 in length is not 18/5 times the 5 inch length. That's why the hammer doesn't look weird.

 

[Robb]

Not what I get. Please post your working.

Sorry, -590=-F18cos(30)-5Fsin30)=32.6175

 

[haruspex]

Sorry, -590=-F18cos(30)-5Fsin30)=32.6175

Yes.

 

[haruspex]

The angle you need to use is not 30 degrees but the angle αα\alpha between the force vector and the perpendicular to the line segment ¯¯¯¯¯¯¯¯¯XAXA¯\overline{XA}. You can calculate that angle using geometry, from the information given.

the method Robb used is valid, and quite efficient.

 

[Robb]

Yes.

Dang, nothing like making a mountain out of a mole hill!

 

[andrewkirk]

the method Robb used is valid, and quite efficient.

So it is. I hadn't noticed that.