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?
I got an answer of 45 N*m (which is correct) but I am having trouble with the second question:
What is the magnitude of the torque about his shoulder if he holds his arm straight, but 46.6° below horizontal?
I tried the following but I'm stil confused as to what the answer is.
Knowing the angle, I drew a right triangle and used trig to get the distances, and then I did just what I did for the first part
To calculate the magnitude of the torque about the shoulder when the athlete holds his arm straight but at an angle below horizontal, you need to consider both the weight of the steel ball and the torque due to the weight of the athlete's arm.
Here's how you can approach this problem:
1. Start by calculating the perpendicular distance between the shoulder and the line of action of the weight vector of the steel ball. This perpendicular distance is the effective lever arm for the torque. In this case, it will be the distance from the shoulder to the point where the extended arm intersects with the horizontal line. You can use trigonometry to calculate this distance.
2. Next, calculate the torque due to the weight of the steel ball. This can be done by multiplying the weight of the ball by the lever arm distance calculated in step 1. The weight of the ball can be calculated using the formula: weight = mass x gravity, where gravity is approximately 9.8 m/s².
3. Calculate the torque due to the weight of the athlete's arm. The weight of the arm can be calculated using the formula: weight = mass x gravity. The lever arm for the arm's weight will be half the length of the arm since it is acting at the center of mass.
4. To find the magnitude of the total torque about the shoulder, add the torques calculated in step 2 and step 3.
Here's a step-by-step breakdown of the calculation:
Step 1:
Using trigonometry, calculate the perpendicular distance between the shoulder and the extended arm. If the arm is 46.6° below horizontal, you can use the formula: distance = arm length x sin(angle).
Step 2:
Calculate the torque due to the weight of the ball using the formula:
torque_ball = weight_ball x lever arm.
Step 3:
Calculate the torque due to the weight of the arm using the formula:
torque_arm = weight_arm x lever arm.
Step 4:
Find the magnitude of the total torque by adding the torques from step 2 and step 3:
total torque = torque_ball + torque_arm.
By following these steps and plugging in the appropriate values, you should be able to find the magnitude of the torque about the shoulder when the athlete holds his arm straight but at an angle below horizontal.