A man is holding an 8.00kg vacuum cleaner at arm's length, a distance of .550m from his shoulder. What is the torque on the shoulder joint if the arm is held at 30degrees below the horizontal?
To calculate the torque on the shoulder joint, we need to determine the force exerted by the vacuum cleaner and the distance from the shoulder where the force is applied.
First, let's find the force exerted by the vacuum cleaner. We can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration due to gravity (g):
F = m * g
Given that the mass of the vacuum cleaner is 8.00 kg, and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the force:
F = 8.00 kg * 9.8 m/s² = 78.4 N
Next, we need to find the horizontal component of the force. Since the arm is held at a 30-degree angle below the horizontal, the horizontal component is given by:
F_horizontal = F * cos(theta)
where theta is the angle below the horizontal (30 degrees):
F_horizontal = 78.4 N * cos(30°)
Now, we can calculate the distance from the shoulder joint where the force is applied. The given distance is 0.550 m.
Finally, we can calculate the torque using the following formula:
Torque = F_horizontal * d
where F_horizontal is the horizontal component of the force and d is the distance from the shoulder joint:
Torque = F_horizontal * d
Plugging in the values:
Torque = (78.4 N * cos(30°)) * 0.550 m
Calculating this expression will give you the torque on the shoulder joint.