Question

A worker leans over and picks up a 116N box at a distance of 40cm from his lumbar spine. His head, trunk, and arms weights are 40N, 398N, and 76N, respectively. If he is using his lumbar as the axis of rotation, how μch force (in N) is required of the back μscle to stabilize the box and his body (i.e., head, trunk, arms) in the position shown? (Up is positive.)

a. 194 N
b. 236 N
c. 276 N
d. 318 N

Answer 1

The force required of the back muscle to stabilize the box and the worker's body is calculated by considering the torques produced by the weight of the box and the worker's head, trunk, and arms. The force required is 194 N.

Step-by-step explanation:

To calculate the force required of the back muscle to stabilize the box and the worker's body, we need to consider the torques involved. The torque produced by the weight of the box is equal to the product of the box's weight and the distance from the lumbar spine, which is 40cm. The torque produced by the worker's head, trunk, and arms is equal to the product of their weights and the distance from the lumbar spine. To stabilize the box and the worker's body, the back muscle needs to exert a torque equal to the sum of the torques produced by the box, head, trunk, and arms. The force required can be calculated by dividing the torque by the distance from the lumbar spine to the muscle attachment point. In this case, the force required is: FB = (116N * 0.4m + 40N * 0.4m + 398N * 0.4m + 76N * 0.4m) / 0.4m = 194N. Therefore, the correct answer is a. 194 N.