Final answer:
To calculate the torque required by the quadricep muscles to hold maximal knee extension, one would sum the torques produced by the ankle weight, the weight of the lower leg, and the hamstring muscle, considering their respective forces and lever arms. The net torque is found to be 27 N·m.
Step-by-step explanation:
The question given is asking about the generation of torque by the muscles in the human body, specifically the quadriceps, during the action of holding the knee in extension against various forces. To find the torque required by the quadricep muscles, we have to consider the torques applied by the ankle weight, the weight of the lower leg, and the hamstring muscle force.
The torque (τ) exerted by a force can be calculated using the equation τ = r * F * sin(θ), where r is the lever arm distance, F is the force applied and θ is the angle between the force vector and the lever arm. In this situation, all the forces are perpendicular to the lever arms, thus the angle (θ) will be 90° and sin(θ) will be 1, simplifying the calculation because the sin(90°) = 1.
Here are the calculated torques for each force:
- Ankle weight torque: 150 N * 0.30 m = 45 N·m
- Lower leg weight torque: 200 N * 0.15 m = 30 N·m
- Hamstring muscle force torque: -800 N * 0.06 m = -48 N·m (negative because it opposes the quadricep torque)
Now, we sum the torques to find the net torque that the quadricep muscle must produce to hold the leg in place:
Net torque = 45 N·m + 30 N·m - 48 N·m = 27 N·m. This is the torque that the quadricep muscle needs to generate to hold maximal knee extension.