Woman standing on ball of foot - torque

[superdave]

Now consider a woman standing on the ball of her foot as shown. A normal force of magnitude N acts upward on the ball of her foot. The Achilles' tendon is attached to the back of the foot. The tendon pulls on the small bone in the rear of the foot with a force F. This small bone has a length x, and the angle between this bone and the Achilles' tendon is phi. The horizontal displacement between the ball of the foot and the point P is D.

Find Torque_N about point P due to normal force.

Express in terms of N and any other quantities given.

So, help?

 

[NateTG]

Seems pretty straightforward. How do you calculate torque?

 

[superdave]

Distance to pivot point * moment arm * force?

I know the distance is sqrt(N^2+D^2), the force is N. But then the moment arm I'm having trouble with. It's sin of the angle, but we don't have the angle. But the sin should be (N/sqrt(N^2+D^2)) Opposite over Hypotenuse. But that's not it.

 

[NateTG]

It's the sine of the angle between the lever arm and the force, so N is the adjacent side, and D is the opposite side.

 

[Traak]

OP, I was in the same mindset you were in when I first attempted this problem. It is actually not that complicated if you look past the common formulas. To get the moment arm you drop a perpendicular line from the force to the pivet point. The normal force is pointing straight up so dropping a 90 degree line is actually the "D" variable already given.

So knowing that Torque = Force * (moment arm) it is simply N *- D.