Finding the center of gravity & mass by torque?

[garfiegrl]

I don't know how to do these kinds of problems; I just need an example of one, could someone just work it out with an explanation?
Feel free to change the values or whatever.
This particular problem isn't to turn in, I'm studying for a test on this material.

A meter stick is pivoted the 50-cm mark but does not balance because of nonconformities in material.
150 g and 200 g weights ar placed at the 10-cm and 75-cm marks to balance the meterstick.
When the weights are interchange, the pivot point is at the 43-cm mark.
find the mass of the stick and the center of gravity.

 

[Doc Al]

You already have a thread on this problem in Intro Physics. Please continue discussion there.

 

[astrokreng]

To find the center of gravity and mass by torque, we can use the equation: Torque = Force x Distance. In this case, the force is the weight of the weights and the distance is the distance from the pivot point to where the weights are placed. We can set up the following equation for each weight:

Torque1 = (150 g) x (40 cm) = 6000 g*cm
Torque2 = (200 g) x (5 cm) = 1000 g*cm

Since the meter stick is not balanced, the torques must be equal but opposite in direction. This can be represented as:

Torque1 = -Torque2
6000 g*cm = -1000 g*cm

To find the mass of the stick, we can use the equation: Total torque = (mass of stick) x (distance to center of gravity). We know the total torque (6000 g*cm) and the distance to the center of gravity (43 cm), so we can solve for the mass of the stick:

6000 g*cm = (mass of stick) x (43 cm)
mass of stick = 139.5 g

To find the center of gravity, we can use the equation: Distance to center of gravity = (Total torque) / (mass of stick). Plugging in the values, we get:

Distance to center of gravity = 6000 g*cm / 139.5 g = 43 cm

Therefore, the center of gravity is located at the 43-cm mark from the pivot point. This means that the nonconformities in material are causing the center of gravity to shift from the expected 50-cm mark.

In summary, by using the principles of torque, we were able to find the mass of the stick and the location of the center of gravity, even with the nonconformities in material. This method can be applied to any object with a known weight and distance to find its center of gravity and mass.