Final answer:
To calculate the force exerted by the biceps brachii when attaching at a 90-degree angle to the radius 3 cm from the elbow joint, you need to know the mass of the object being lifted and apply the torque equilibrium principle using the formula τ = r × F × sin(θ).
Step-by-step explanation:
The calculation of the force exerted by the biceps muscle involves understanding the biomechanics of the arm and applying principles of physics, specifically torque.
To calculate the force produced by the biceps brachii, we need to consider the moment of inertia of the forearm, the weight lifted (or force applied), and the perpendicular distance from the force application to the center of rotation, which in this case is the elbow joint.
When a biceps muscle attaches at a 90-degree angle to the radius at 3 cm from the elbow joint, the torque created by the muscle can be calculated using the formula τ = r × F × sin(θ), where τ is the torque, r is the radius or lever arm (3 cm in this case), F is the force, and θ is the angle of application (90 degrees here, which means sin(θ) = 1 since sin(90°) = 1).
Example Calculation
For example, if a 5.0 kg weight is lifted, the force due to gravity is F = m × g, where m is the mass (5.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
This gives a force of 5.0 kg × 9.8 m/s² = 49 N. To keep the forearm and the weight stationary, the torque produced by the muscle needs to counteract the torque due to the weight of 5.0 kg.
Assuming the distance from the elbow joint to the hand (where the weight is held) is 24.0 cm (0.24 m), the torque due to the weight is 49 N × 0.24 m. To find the force exerted by the biceps brachii, we solve for F in the formula for torque assuming it's producing an equal and opposite torque to hold the weight stationary.