How Do Forces Determine the Balance of a Supported Ruler?

[Miri]

Homework Statement

A ruler of 0.75N and 52.0cm is supported 1.0cm from each of its two ends. A weight of 1.00N is placed 16.0cm from the left end of the ruler. Determine the forces acting upon the ruler at the two supports.

Homework Equations

I know that the two forces of the supports are pointing upward and 1.00N is pointing downward as well as 0.75N. So I know that the two forces of the supports together are 1.75N. But I don't know what to do now.

 

[Hootenanny]

Homework Statement

A ruler of 0.75N and 52.0cm is supported 1.0cm from each of its two ends. A weight of 1.00N is placed 16.0cm from the left end of the ruler. Determine the forces acting upon the ruler at the two supports.

Homework Equations

I know that the two forces of the supports are pointing upward and 1.00N is pointing downward as well as 0.75N. So I know that the two forces of the supports together are 1.75N. But I don't know what to do now.

HINT: Consider the moments (or torques) about one of the pivots.

 

[nlightner]

To determine the forces acting upon the ruler at the two supports, we can use the principle of moments, which states that the sum of the moments acting on an object must be equal to zero for it to be in equilibrium.

First, let's calculate the moment of the weight (1.00N) about the left support (1.0cm from the left end of the ruler). This can be calculated by multiplying the weight by its distance from the support:

Moment of weight = 1.00N x 16.0cm = 16.00 Ncm

Next, let's calculate the moment of the ruler's weight (0.75N) about the left support. Since the ruler is in equilibrium, the sum of the moments must be equal to zero, so we can set up the following equation:

16.00 Ncm = 0.75N x d

Where d is the distance between the left support and the weight (16.0cm - 1.0cm = 15.0cm). Solving for d, we get:

d = 16.00 Ncm / 0.75N = 21.33 cm

This means that the distance between the left support and the weight is 21.33 cm. Now, we can calculate the force acting on the left support by dividing the moment of the weight by the distance between the support and the weight:

Force on left support = 16.00 Ncm / 21.33 cm = 0.75N

Similarly, we can calculate the force on the right support by dividing the moment of the ruler's weight by the distance between the right support and the weight (16.0cm - 21.33cm = -5.33cm):

Force on right support = 16.00 Ncm / -5.33 cm = -3.00N

Therefore, the forces acting on the ruler at the two supports are 0.75N (upward) on the left support and -3.00N (downward) on the right support. This shows that the ruler is in equilibrium, as the sum of the forces is equal to zero (0.75N + (-3.00N) = 0.75N - 3.00N = -2.25N + 2.25N = 0N).

I hope this helps to clarify the calculation process. Keep up the