A man holds a 178 -N ball in his hand, with the forearm...

A man holds a 178 -N ball in his hand, with the forearm horizontal (see the drawing), He can support the ball in this position because of the flexor muscle force $\mathbf{M}$, which is applied perpendicular to the forearm. The forearm weighs $22.0 \mathrm{N}$ and has a center of gravity as indicated. Find (a) the magnitude of $\mathbf{M}$ and (b) the magnitude and direction of the force applied by the upper arm bone to the forearm at the elbow joint.

Key Concepts

Moment Arm

The moment arm is the perpendicular distance from the axis of rotation (in this case, the elbow joint) to the line of action of the force. Accurate identification of moment arms for different forces acting on the forearm is essential for correctly calculating the torques and thereby analyzing the equilibrium conditions.

Center of Gravity

The center of gravity is the point at which the entire weight of an object can be considered to act. In biomechanics and statics problems, identifying the center of gravity of an object—in this case, the forearm—allows one to accurately determine the torque produced by its weight about a chosen pivot point, which is crucial for establishing equilibrium.

Static Equilibrium

Static equilibrium refers to the condition in which all forces and moments (torques) acting on a system balance such that the system remains at rest. In problems like the given scenario, ensuring that both the net force and the net torque are zero is essential to determining unknown forces or moments, as the forearm maintains its horizontal position without rotational or translational movement.

Torque (Moment of Force)

Torque is the measure of the rotational effect of a force about a pivot or axis, calculated as the product of the force and its perpendicular distance (moment arm) from the pivot. In this problem, the muscle force and weights produce torques about the elbow, and balancing these torques is key to solving the mechanics of the forearm.

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