An athlete is supporting a weight of 200N in his hand with his forearm at a

right angle to his biceps. Assuming his biceps are in the vertical plane, the
axis of rotation of the forearm is 3 cm from the elbow and 25 cm from the
centre of gravity of the weight, calculate the force that must be produced by
the biceps to hold the weight. [8 marks]

To calculate the force that must be produced by the biceps to hold the weight, we need to consider the principles of torque and equilibrium.

Torque, or moment of force, is the concept of a force causing rotational motion. It is calculated by multiplying the force applied by the perpendicular distance from the axis of rotation to the line of action of the force. The formula for torque is as follows:

Torque = Force x Distance

In this case, the force is the weight being supported by the athlete's hand (200N), and the distance is the perpendicular distance from the axis of rotation to the line of action of the force.

Given that the axis of rotation is 3 cm from the elbow and 25 cm from the center of gravity of the weight, we can calculate the total distance by adding these two distances:
Total Distance = Distance from elbow to axis of rotation + Distance from axis of rotation to center of gravity
Total Distance = 3 cm + 25 cm = 28 cm = 0.28 m (converting to meters)

Now we can calculate the torque exerted by the weight being supported:

Torque = Force x Distance
Torque = 200N x 0.28m
Torque = 56 Nm

The torque exerted by the weight being supported is 56 Nm.

This torque is countered by the torque produced by the biceps. Since the forearm is at a right angle to the biceps, the perpendicular distance from the axis of rotation to the biceps is the same as the total distance calculated earlier (0.28 m).

Now, let's calculate the force exerted by the biceps:

Torque = Force x Distance
56 Nm = Force x 0.28m

Solving for force, we have:

Force = Torque / Distance
Force = 56 Nm / 0.28m
Force = 200 N

Therefore, the force that must be produced by the biceps to hold the weight is 200 N.