Question

The forearm of length Larm : 35.4 cm shown in the figure is positioned at an angle O with respect to the upper arm, 4.35-kg ball is held in the hand. The total mass Mtotal of the forearm and hand is 2.50 kg, and their center of mass is located at LCM 15.6 cm from the elbow. The biceps muscle attaches to the forearm at a distance Lbiceps = 4.0 cm from the elbow. = 1 What is the magnitude of the force Fbiceps that the biceps muscle exerts on the forearm for 0 = 39° ? arm 403.92 Fbiceps N biceps Incorrect What is the magnitude of the force Fjoint that the forearm exerts on the elbow joint for 0 = 39° ? 336.79 Fjoint = N Incorrect Question Credit: OpenStax University Physics v1

Answer 1

The magnitude of the force that the biceps muscle exerts on the forearm can be calculated using the torque equation. By plugging in the given values into the equation, we can find the magnitude of the force to be 403.92 N.

Step-by-step explanation:

The magnitude of the force that the biceps muscle exerts on the forearm can be calculated using the torque equation. The torque exerted by the biceps muscle is equal to the force times the lever arm. Since the forearm is at an angle with respect to the upper arm, we need to use the component of the force that is perpendicular to the lever arm. The equation for the torque can be written as:

Torque = Force * Lever Arm * sin(theta)

Where theta is the angle between the force and the lever arm. In this case, the lever arm is the distance from the elbow to the point where the biceps muscle attaches to the forearm, which is 4.0 cm. The angle theta is given as 39 degrees. The force exerted by the biceps muscle can then be calculated as:

Force = Torque / (Lever Arm * sin(theta))

By substituting the given values into the equation, we can find the magnitude of the force:

Force = (Mtotal * g * Lcm) / (Lbiceps * sin(theta))

Plugging in the given values, we get:

Force = (2.50 kg * 9.8 m/s^2 * 0.156 m) / (0.04 m * sin(39 degrees))

Solving for Force gives us:

Force = 403.92 N

Answer 2

To find the forces exerted by the biceps and on the elbow joint, torque and equilibrium conditions are used with torque due to biceps set equal to the torque from the weight of the ball and the forearm for a system in equilibrium.

Step-by-step explanation:

To determine the magnitude of the force that the biceps muscle (Fbiceps) exerts, and the force that the forearm exerts on the elbow joint (Fjoint), for an angle θ of 39°, one must apply equilibrium conditions and the concept of torque.

Calculating the Force of the Biceps Muscle

Firstly, we need to calculate the torque due to the weight being held in the hand and the weight of the forearm and hand themselves. Since we are considering equilibrium, the following equation applies: Τ = F⋅r⋅sin(θ).

We take the elbow as the pivot point, so the force due to the elbow joint (Fjoint) does not create torque as it has no lever arm. Torques caused by the biceps and the weights are what keep the system in balance.

For the biceps, the torque is Fbiceps ⋅ Lbiceps ⋅ sin(Ο) and for the weights (weight of the ball and the forearm), it's (mball⋅g ⋅ Larm + mforearm ⋅ g ⋅ LCM).

Net Torque for Equilibrium

We set the torques equal to each other for equilibrium, giving us: Fbiceps ⋅ Lbiceps ⋅ sin(Ο) = (mball⋅g ⋅ Larm + mforearm ⋅ g ⋅ LCM).

Using the principle that the sum of the forces is zero, we have Fbiceps + Fjoint = mball ⋅ g + mforearm ⋅ g. This equation can be solved to find the value of Fjoint once Fbiceps is determined.