a person holds a 5 kg mass in his hand. the forearm is held 45 degrees below the horizonal. the biceps muscle isa attached 5cm from the elbow ad th eight is held 35 cm from the elbow. neglecting mass of the forearm find the tension in the bicep muscle.
To find the tension in the bicep muscle, we need to consider the forces acting on the mass held by the person.
First, let's define the coordinate system. Let the positive x-axis be horizontal, pointing to the right, and let the positive y-axis be vertical, pointing upwards.
When the forearm is held at a 45-degree angle below the horizontal, it forms an angle of 45 degrees with the y-axis. The weight of the mass acts vertically downward, opposite to the positive y-direction.
Next, we need to resolve the weight of the mass into its components. The weight force can be decomposed into two perpendicular components: one parallel to the forearm and one perpendicular to the forearm.
The component parallel to the forearm exerts a force along the x-axis, and the component perpendicular to the forearm exerts a force along the y-axis.
The component parallel to the forearm can be found using the sine function:
F_parallel = mass × g × sin(angle)
where mass is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and angle is the angle formed by the forearm with the horizontal (45 degrees in this case).
F_parallel = 5 kg × 9.8 m/s^2 × sin(45 degrees)
≈ 5 kg × 9.8 m/s^2 × 0.707
≈ 34.49 N (rounded to two decimal places)
The component perpendicular to the forearm can be found using the cosine function:
F_perpendicular = mass × g × cos(angle)
F_perpendicular = 5 kg × 9.8 m/s^2 × cos(45 degrees)
≈ 5 kg × 9.8 m/s^2 × 0.707
≈ 34.49 N (rounded to two decimal places)
Now, consider the forces acting on the mass held by the person. We have two forces: the tension force in the bicep muscle and the perpendicular component of the weight.
The tension force in the bicep muscle pulls the forearm upward and opposes the component perpendicular to the forearm. Therefore, the tension force T equals the perpendicular component of the weight.
T = F_perpendicular
= 34.49 N (rounded to two decimal places)
Therefore, the tension in the bicep muscle is approximately 34.49 Newtons.