Biomechanics question: Need help with this lab

[kae3210]

Homework Statement

A person is sitting and extending the knee at an angle of 45 degrees.
The mass of the person is 98 kg, the lower leg length is 44 cm and the location of the weight is 40 cm with respect to the knee.
Assumptions:
The mass of the lower leg and foot is 5.8% of total body mass. Assume this mass acts at distance of 15 cm from the knee joint.
• The knee extensors insert at an angle of 15º to the long axis of the leg and that this attachment is 4.5 cm from the knee joint center.
Assume the ankle weight that is on the ankle is 20kg.
• What is knee extensor force required to keep the knee at 45º?

Homework Equations

I don't even know. I'm guessing that it's these.

Sum of moments = 0
Sum of forces = 0

The Attempt at a Solution

I drew a free body diagram but that's as far as I get...

 

[KataKoniK]

Thank you for your post. I would like to help you find the solution to your problem.

First, let's define the variables we will be using:
- Mass of the person (m) = 98 kg
- Mass of lower leg and foot (m_leg) = 5.8% of total body mass = 5.684 kg
- Length of lower leg (l) = 44 cm
- Distance of weight from knee joint (d) = 40 cm
- Distance of lower leg mass from knee joint (d_leg) = 15 cm
- Angle of knee extension (θ) = 45 degrees
- Angle of knee extensor insertion (α) = 15 degrees
- Distance of knee extensor insertion from knee joint (d_ext) = 4.5 cm
- Weight on ankle (W) = 20 kg

Now, let's consider the forces acting on the knee joint. There are two main forces: the force from the weight of the person and the force from the weight on the ankle. The force from the weight of the person can be calculated using the formula F = mg, where g is the acceleration due to gravity (9.8 m/s^2). Therefore, the force from the weight of the person is F_person = (98 kg)(9.8 m/s^2) = 960.4 N.

Next, let's consider the force from the weight on the ankle. This force acts at a distance of 44 cm from the knee joint, and it can be calculated using the formula F = Wd/l, where W is the weight on the ankle, d is the distance from the knee joint, and l is the length of the lower leg. Therefore, the force from the weight on the ankle is F_ankle = (20 kg)(44 cm)/(44 cm) = 20 kg x 9.8 m/s^2 = 196 N.

Now, we need to consider the force from the lower leg mass. This force acts at a distance of 15 cm from the knee joint and at an angle of 15 degrees to the long axis of the leg. To calculate this force, we can use the formula F = m_leg x g x sin(α) x (d_leg/d), where m_leg is the mass of the lower leg and foot, g is the acceleration due to gravity,