Solve Biomechanics Problem: Find Fk & Tk Answers

[tl_glover]

Homework Statement

Please help, anyone. This is not homework as such but rather it is for test preparation.

The biomechanics problem with diagrams is here: http://oregonstate.edu/instruct/exss323/Xtra_Problem4.pdf"

As you will note, the answers are already provided. I am only interested in how to come to the answers for parts A and B.

Homework Equations

Resultant joint force= The vector sum of all forces acting across a joint.

Resultant joint torque= The sum of the torques

How do we find Fk when angles are involved? Thats throwing me off. Tk also.

The Attempt at a Solution

I already know that the direction of B is clockwise just by looking at the diagram, and that the hamstrings are involved in C.

The Fk and Tk answers are in the above link already but how to get to them is completely uncertain? I am looking for the right process to complete come to the answers provided.

Someone please help :( Thanks

 

[cepheid]

Welcome to PF,

You have three unknowns: F_kx, F_ky, and T_k. However, you also have three equations, therefore you can arrive at an exact solution. You have three equations because you know the system is in equilibrium:

∑F_x = 0
∑F_y = 0
∑T = 0

The first equation can be written as follows:

F_kx + F_Ax = 0

Finding F_Ax, the horizontal component of the force applied to the ankle, is the only tricky part. To do this, you need to figure out what angle F_A makes with the horizontal. This just requires some thought in order to understand the geometry of the situation, but it's not hard.

The equation for the sum of the vertical forces will be similar. For the equation for the sum of torques, again you'll have to pay close attention to the geometry in order to get the lever arms right.

For future reference, questions like this should be posted in Intro Physics.