Physics Question Has Me Stumped. Help Please?

Question

After a skiing accident, your leg is in a cast and supported in a traction device, as shown in Figure 6-27. Find the magnitude of the force F exerted by the leg on the small pulley. (By Newton's third law, the small pulley exerts an equal and opposite force on the leg.) Let the mass m be 3.30 kg, and the angle be 29.0°.

Figure:
http://i190.photobucket.com/albums/z204/inthisdarcness/06-22alt.gif

Please help if you can. I have worked at it, but I get the wrong answer everytime.

Answer 1

good ol' statics

i'll provide the method, you can plug in the numbers.

A FBD of the mass
Sum of the vertical forces = 0
0 = T2 - m*g

T2 = m*g

Sum of the forces along F's direction at the pulley = 0

0 = T2*cos(theta) + T1*cos(theta) - F

Sum of the forces perpendicualr to F's direction at the pulley = 0

0 = T1*sin(theta) - T2*sin(theta)

T1 = T2

Sub back into the top

0 = T2*cos(theta) + T2*cos(theta) - F

F = 2*T2*cos(theta)

Remeber, T2 = m*g

F = 2 * m*g*cos(theta)

Answer 2

T1 = T2 = T. If not the pulley will move in the direction of greater force.
Resolving T,
F = 2T cos θ.
Since m is at rest, T = Mg.
F = 2m g cos θ.
F = 2* 3.3 *9.8 cos 29 = 56.57 N.