An athlete at the gym holds a 4.33 kg steel ball in his hand. His arm is 68.7 cm long and has a mass of 4.69 kg. What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor?
Torque = massball x g + massarm x g/2
= 4.33 kg x 9.8 + 4.69 kg x 9.8/2
= 42.434 + 22.981
= 65.415 N
Why is my answer incorrect?
Your answer is incorrect because to failed to include the length of his arm when calculating the torque. Your answer has the dimension of force, not torque.
The factor of 1/2 is correct for the torque due to the weight of his arm, IF the arm has uniform mass per unit length. Most arms do not, but they probably want you to assume that.
Your answer is incorrect because you did not correctly calculate the torque formula. The formula for torque is torque = force x lever arm.
To find the torque in this situation, you need to multiply the force exerted by the mass of the ball by the lever arm, which is the distance between the point of rotation (shoulder) and the point where the force is applied (center of mass of the ball).
Let's go through the calculations step by step:
Mass of the ball (m_ball) = 4.33 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Distance between the shoulder and center of mass of the ball (lever arm, L) = 68.7 cm = 0.687 m
Now we can calculate the torque:
Torque = force x lever arm
To find the force exerted by the mass of the ball, we can use Newton's second law (F = ma):
Force exerted by the ball (F_ball) = m_ball x g
Substituting the given values:
F_ball = 4.33 kg x 9.8 m/s^2 = 42.434 N
Finally, we can calculate the torque:
Torque = F_ball x L
Torque = 42.434 N x 0.687 m ≈ 29.15 Nm
Therefore, the correct magnitude of the torque about the shoulder is approximately 29.15 Nm, not 65.415 N as calculated in your response.