An athlete at the gym holds a 4.33 kg steel ball in his hand. His arm is 75.0 cm long and has a mass of 5.28 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?
Responses
Physics - bobpursley, Saturday, October 11, 2008 at 9:36pm
The torque has to be the weight of the ball x distance plus the weight of the arm x 1/2 the length of the arm(assuming the cg is at the midpoint).
Is distance 0.75 m?
What distance? The arm length is 0.75 m, but half of that is 0.375 m
If you want torque in units of Newton-meters, the lengths must be in meters when you do the calculation
To find the magnitude of the torque, we need to consider the weight of the ball and the weight of the arm.
First, let's calculate the torque due to the weight of the ball. The weight of an object is given by the formula weight = mass x acceleration due to gravity. In this case, the mass of the steel ball is 4.33 kg. The acceleration due to gravity is approximately 9.8 m/s^2. So, the weight of the ball is:
Weight of the ball = mass of the ball x acceleration due to gravity
= 4.33 kg x 9.8 m/s^2
Next, we need to calculate the distance from the shoulder to the point where the ball is being held. The given length of the athlete's arm is 75.0 cm, which is equivalent to 0.75 m.
Now, we can calculate the torque due to the weight of the ball, using the formula torque = force x distance:
Torque due to the weight of the ball = Weight of the ball x distance
= (4.33 kg x 9.8 m/s^2) x 0.75 m
Next, let's calculate the torque due to the weight of the arm. The weight of the arm is given by the formula weight = mass x acceleration due to gravity. In this case, the mass of the arm is 5.28 kg.
Now, we need to calculate half the length of the arm, assuming the center of gravity is at the midpoint. Since the length of the arm is already given as 75.0 cm or 0.75 m, half the length would be 0.375 m.
Finally, we can calculate the torque due to the weight of the arm:
Torque due to the weight of the arm = Weight of the arm x 1/2 the length of the arm
= (5.28 kg x 9.8 m/s^2) x 0.375 m
To calculate the total torque, we can add the torques due to the weight of the ball and the weight of the arm:
Total torque = Torque due to the weight of the ball + Torque due to the weight of the arm
Now, you can substitute the values into the formulas and calculate the magnitude of the torque about the shoulder.