Question

a man is holding an 8.00-kg vacuum cleaner at arm's length, a distance of 0.550 m from his shoulder. what is the torque on the shoulder joint if the arm is horizontal?\

Answer 1

The torque on the shoulder joint when holding an 8.00-kg vacuum cleaner at arm's length is 43.12 N·m.

Step-by-step explanation:

The torque on the shoulder joint can be calculated using the equation:

Torque = Force x Lever Arm

Since the vacuum cleaner is being held at arm's length, the force is simply the weight of the vacuum cleaner, which can be calculated using the equation:

Force = mass x acceleration due to gravity

Given that the mass of the vacuum cleaner is 8.00 kg and the acceleration due to gravity is 9.8 m/s², the force on the shoulder joint is:

Force = 8.00 kg x 9.8 m/s² = 78.4 N

The lever arm is the distance from the shoulder joint to the vacuum cleaner, which is given as 0.550 m.

Therefore, the torque on the shoulder joint is:

Torque = 78.4 N x 0.550 m = 43.12 N·m

Answer 2

The torque on the shoulder joint is 42.96 N.m.

Step-by-step explanation:

To calculate the torque on the shoulder joint, we need to multiply the force exerted by the distance from the pivot point. In this case, the force is the weight of the vacuum cleaner, which is equal to its mass multiplied by the acceleration due to gravity. The distance from the pivot point is given as 0.550 m. Therefore, the torque can be calculated as:

Torque = force x distance = (mass x gravity) x distance = (8.00 kg x 9.8 m/s^2) x 0.550 m = 42.96 N.m