What is the Mass of the Ruler on a Sharp Edge?

[Miri]

Turning effects of forces 3

Homework Statement

A ruler of an unknown mass is 52.0cm long. To find out its mass, you put a stone of 100g on the ruler 3.0cm from its end and balance the ruler on a sharp edge. The ruler is balanced when the supporting edge is 15.0cm from its end. Calculate the mass of the ruler.

Homework Equations

I know that the force of the stone is 0.981N. But what do I have to do to find out the force pointing downward of the ruler, so that I can find the mass...?

 

[Hootenanny]

Homework Statement

A ruler of an unknown mass is 52.0cm long. To find out its mass, you put a stone of 100g on the ruler 3.0cm from its end and balance the ruler on a sharp edge. The ruler is balanced when the supporting edge is 15.0cm from its end. Calculate the mass of the ruler.

Homework Equations

I know that the force of the stone is 0.981N. But what do I have to do to find out the force pointing downward of the ruler, so that I can find the mass...?

This question is very similar to your other thread, turning forces 4 and can be tackled in a very similar manner.

 

[nlightner]

To find the mass of the ruler, we can use the principle of moments. This principle states that the sum of the clockwise moments must be equal to the sum of the anticlockwise moments for an object to be in equilibrium. In this case, the clockwise moment is the force of the stone (0.981N) multiplied by its distance from the fulcrum (3.0cm), and the anticlockwise moment is the unknown downward force of the ruler multiplied by its distance from the fulcrum (15.0cm).

Using this principle, we can set up the equation: 0.981N x 3.0cm = F x 15.0cm, where F is the unknown downward force of the ruler. Solving for F, we get F = 0.1962N.

To find the mass of the ruler, we can use Newton's Second Law, which states that force is equal to mass multiplied by acceleration. In this case, the acceleration is due to gravity (9.8m/s^2). Therefore, the mass of the ruler is 0.1962N/9.8m/s^2 = 0.02kg or 20g.

In conclusion, the mass of the ruler is 20g.