A person holds a 1.42N baseball in his hand, a distance of 34.0cm from the elbow joint, as shown in the figure . The biceps, attached at a distance of 2.75cm from the elbow, exerts an upward force of 12.6N on the forearm. Consider the forearm and hand to be a uniform rod with a mass of 1.25kg.
a. Calculate the net torque acting on the forearm and hand. Use the elbow joint as the axis of rotation.
Net torque = (1.42N)(34.0cm) - (12.6N)(2.75cm) = 44.9 Nm
To calculate the net torque acting on the forearm and hand, we need to understand that torque is defined as the force applied perpendicular to the axis of rotation multiplied by the distance from the axis.
In this case, we have two forces acting on the forearm and hand:
1. The weight of the baseball, which is acting downward with a force of 1.42 N.
2. The force exerted by the biceps, which is acting upward with a force of 12.6 N.
We also need to know the distances from the axis of rotation (the elbow joint) to each force:
1. The distance from the elbow joint to the baseball is 34.0 cm, which is equal to 0.34 m.
2. The distance from the elbow joint to the biceps is 2.75 cm, which is equal to 0.0275 m.
Now we can calculate the net torque acting on the forearm and hand:
Torque due to the weight of the baseball = force × distance
= 1.42 N × 0.34 m
Torque due to the force exerted by the biceps = force × distance
= 12.6 N × 0.0275 m
Net torque = Sum of the torques
= torque due to the weight of the baseball + torque due to the force exerted by the biceps
Now you can calculate the net torque by substituting the values into the equations and adding them up.
To calculate the net torque acting on the forearm and hand, we need to use the equation:
Torque = Force × Distance × sin(θ)
Here, the distance will be the distance between the axis of rotation (elbow joint) and the point where the force is applied. The force is acting at the hand holding the baseball. The angle (θ) between the force and the lever arm can be assumed to be 90 degrees since the force is acting vertically upward.
Given values:
Force (F) = 1.42 N
Distance (r) = 34.0 cm = 0.34 m
Angle (θ) = 90 degrees = π/2 radians
Now, substituting these values into the equation:
Torque = 1.42 N × 0.34 m × sin(π/2)
= 0.48 N·m
Therefore, the net torque acting on the forearm and hand is 0.48 N·m.