The tangential force method involves finding the component of theapplied force that is perpendicular to the displacement from thepivot point to where the force is applied. This perpendicularcomponent of the force is called the tangential force.

(a) What is F_t, the magnitude of the tangential forcethat acts on the pole due to the tension in the rope?
Express your answer in terms ofT and theta.

When using the tangential force method, you calculate the torqueusing the equation

\tau = f_{\rm t} d,

where d is the distance from the pivot tothe point where the force is applied. The sign of the torque can bedetermined by checking which direction the tangential force wouldtend to cause the pole to rotate (where counterclockwise rotationimplies positive torque).

(b) What is the magnitude of the torque tau on the pole, about point A, due to thetension in the rope?
Express your answer in terms ofT, L, and theta.

The moment arm method involves finding the effective moment armof the force. To do this, imagine a line parallel to the force,running through the point at which the force is applied, andextending off to infinity in either direction. You may shift theforce vector anywhere you like along this line without changing thetorque, provided you do not change the direction of the forcevector as you shift it. It is generally most convenient to shiftthe force vector to a point where the displacement from it to thedesired pivot point is perpendicular to its direction. Thisdisplacement is called the moment arm.

For example, consider the force due to tension acting on the pole.Shift the force vector to the left, so that it acts at a pointdirectly above the point A in the figure. The moment arm of theforce is the distance between the pivot and the tail of the shiftedforce vector. The magnitude of the torque about the pivot is theproduct of the moment arm and force, and the sign of the torque isagain determined by the sense of the rotation of the pole it wouldcause.

(c) Find R_m, the length of the moment arm of theforce.
Express your answer in terms ofL and theta.

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

(d) Suppose you were asked to find the torqueabout point P due to the force of magnitude F in the Achilles' tendon. Which of the followingstatements is correct?

Thetangential force method must be used.
The momentarm method must be used.
Eithermethod may be used.
Neithermethod can be used.

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