A Volunteer Suspended by His Arms: Calculating Tension on Lumbar Disc 5

The Approximate Tension on Lumbar Disc 5

The tension on the lumbar disc 5 is equal to the gravitational force acting on the volunteer, which is 784.8 N. Hence, the approximate tension on lumbar disc 5 is 784.8 N.

Understanding the Situation

When a person is suspended by his or her arms, the tension in the lumbar disc 5, which is near his or her center of mass, is affected. In this situation, a volunteer with a mass of 80 kg is suspended by his arms on Earth.

Calculating the Tension

We are supposed to determine the approximate tension on lumbar disc 5 which is situated close to the center of mass. In this case, the tension on the lumbar disc 5 can be calculated using the concept of the center of mass.

The center of mass of the human body lies in front of the second sacral vertebra in the median sagittal plane and is approximately 54.2% of the standing height from the top of the head. In order to calculate the approximate tension on the lumbar disc 5, we can use the principle of moments.

The principle of moments states that when a body is in equilibrium, the sum of the anticlockwise moments equals the sum of the clockwise moments.

The approximate tension on lumbar disc 5 can be calculated using the following steps:We should find out the distance of the lumbar disc 5 from the volunteer's center of mass.

As it is mentioned in the question that the disc is situated near the center of mass, we can assume that the distance between the center of mass and the lumbar disc 5 is 0.2 m.

We know that the gravitational force acting on the volunteer is given by F = m x g, where F is the force, m is the mass of the volunteer, and g is the acceleration due to gravity. Here, F = 80 kg x 9.81 m/s² = 784.8 N

We can find out the tension on the lumbar disc 5 by taking moments about the point where the arms are attached to the body.

If we assume that the arms are horizontal and parallel to the ground, the moment due to the tension on the lumbar disc 5 is zero, as the distance between the point where the arms are attached to the body and the lumbar disc 5 is zero.

Therefore, the tension on the lumbar disc 5 is equal to the gravitational force acting on the volunteer, which is 784.8 N. Hence, the approximate tension on lumbar disc 5 is 784.8 N.