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?

Responses

physics - drwls, Sunday, October 12, 2008 at 11:35am
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

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Torque = the weight of the ball x distance plus the weight of the arm x 1/2 the length of the arm

= 4.33 kg x 0.75 m + 5.28 kg x 0.375 m
= 3.2475 + 1.98
= 5.23 N

What am I doing wrong?

Torque is not measured in Newtons. You failed to include g as a factor to convert mass to weight.

In the given problem, we need to calculate the magnitude of the torque about the athlete's shoulder when he holds a 4.33 kg steel ball in his hand. The arm has a length of 75.0 cm (0.75 m) and a mass of 5.28 kg.

The formula to calculate torque is torque = force * distance. In this case, force refers to the weight of the object and distance refers to the distance from the axis of rotation (shoulder) to the object.

First, let's calculate the torque due to the weight of the ball. The weight of an object can be found using the formula weight = mass * gravity, where gravity is typically 9.8 m/s^2.

Weight of the ball = mass of the ball * gravity
= 4.33 kg * 9.8 m/s^2
= 42.434 N

The distance from the shoulder to the ball is equal to the length of the arm, which is 0.75 m.

Torque due to the weight of the ball = weight of the ball * distance
= 42.434 N * 0.75 m
= 31.8255 N·m

Next, let's calculate the torque due to the weight of the arm. The distance from the shoulder to the center of mass of the arm is half its length, which is (0.75 m) / 2 = 0.375 m.

Weight of the arm = mass of the arm * gravity
= 5.28 kg * 9.8 m/s^2
= 51.744 N

Torque due to the weight of the arm = weight of the arm * distance
= 51.744 N * 0.375 m
= 19.404 N·m

Finally, we can calculate the total torque by adding the torques due to the weight of the ball and the arm.

Total torque = torque due to the weight of the ball + torque due to the weight of the arm
= 31.8255 N·m + 19.404 N·m
= 51.2295 N·m

Therefore, the magnitude of the torque about the athlete's shoulder is 51.23 N·m.

It seems that there was a mistake in the calculation of the torque due to the weight of the arm. The correct calculation should be 51.744 N * 0.375 m = 19.404 N·m, not 1.98 N as mentioned in the previous response.