Mass of Meter Stick

In class we were asked to find the mass of a meter stick by only using a meter stick and a 100g lead weight.

In this picture, the meter stick is balanced, so that means the torques are equal. The counter-clockwise torque equals the clockwise torque, because torque = (force)(lever arm)

In this picture, there is a 100g weight on the far side of the meter stick. The center of gravity stays the same, and the axis of rotation stays the same. The only thing that has changed is...

This picture demonstrates how to solve for the mass of the meter stick. We know gravity (9.8), the mass of the weight (100g or 1kg), how long the stick is (100m), the center of gravity (50m), the axis of rotation (70m) and the lever arms (20m and 30m). 50 is just the remaining mass of the meter stick, but it is not necessary to use in the equations for solving.

To solve for the mass of the meter stick, we first need to have to correct measurements. We know that the weight is 100g or 1kg, but weight is measured in Newtons so we need to do a conversion. 

w=mg

w=(.1)(9.8)

w=.98N

So we now know that the weight weighs 9.8N, and we can use that information in our equation.

torque = (force)(lever arm)

counterclockwise torque = clockwise torque

(force)(lever arm) = (force)(lever arm)

(force) (20) = (.98) (30)

20force = 29.4

force = 29.4/20

force = 1.47N

The question asked for the MASS of the meter stick, so we need to convert 1.47N back to mass.

w=mg

1.47 = (m)(9.8)

m = 1.47/9/8

m = 1.5kg

m=150g

The mass of the meter stick is 150g