Question

Aman holds a 171-N ball in his hand, with the forearm horizontal (see the figure). He can support the ball in this position because of the flexor muscle force Ñ , which is applied perpendicular to the forearm. The forearm weighs 20.8 N and has a center of gravity as indicated. Find (a) the magnitude of M and the (b) magnitude and (c) direction (as a positive angle counterclockwise from horizontal) of the force applied by the upper arm bone to the forearm at the elbow joint. Upper arm bone - Flexor muscle M Elbow joint 0.0510 m 0.0890 m -0.330 m (a) Number i Units (b) Number i Units (c) Number i Units

Answer 1

The physics question involves calculating the muscle force and elbow joint force needed to hold a weight with the forearm, applying the principles of equilibrium to find torque balance.

Step-by-step explanation:

The student's question involves understanding the forces and torques acting on a forearm when holding a weight at a specific position. To solve the problem, we will apply the condition of equilibrium, where the sum of torques around a pivot point (the elbow joint) must be zero. Given the weight of the ball, the weight of the forearm, and the distances from the elbow joint, we can calculate the muscle force (M) needed to keep the forearm horizontal. The forces applied by the flexor muscle and the upper arm bone at the elbow generate torques that are counterbalanced by the torques due to the weight of the ball and the weight of the forearm.

Considering the geometry of the forearm and the data provided, we can calculate the required magnitudes of forces and the direction of the force at the elbow joint by setting up equations representing the balance of torques and solving for the unknowns. The direction of the force exerted by the upper arm bone will be directly related to the equilibrium of forces in the vertical direction.

Answer 2

The magnitude of the muscle force and the force at the elbow joint can be calculated by applying equilibrium conditions, considering the torques caused by the ball's weight, the forearm's weight, and the muscle force around the elbow.

Step-by-step explanation:

Calculating the magnitude of the flexor muscle force and the force exerted by the upper arm bone at the elbow requires applying the principles of equilibrium, where the sum of the torques around the elbow must be zero. We consider the weight of the ball and the weight of the forearm as forces that apply torques on different sides of the elbow, and the muscle force as the balancing torque.

To find the magnitude of the flexor muscle force (M), we can set up the equation: M * 0.0510 m = 171 N * 0.330 m + 20.8 N * 0.0890 m. From this equation, we can solve for M. To find the force at the elbow, we sum up the vertical components of the forces, which includes the weight of the ball, the weight of the forearm, and the upward force from the muscle. The direction of the force at the elbow joint is opposite to the force exerted by the muscle, and it's typically upwards (towards zero degrees from horizontal).