Calculating unknown forces using the principle of moments.

In summary: Plug in 1000 and get 650g.In summary, the uniform metre ruler is balanced horizontally on a knife edge at its 350mm mark, by placing a 3.0N weight on the rule at its 10mm mark. The weight of the ruler is 650g.
  • #1
Craptola
14
0
Hello, run into a bit of a stumbling block studying moments perhaps someone could nudge me in the right direction.

Homework Statement


A uniform metre ruler is balanced horizontally on a knife edge at its 350mm mark, by placing a 3.0N weight on the rule at its 10mm mark. Calculate the weight of the ruler.


Homework Equations


Not entirely certain but I have to assume it involves
Moments = force x perpendicular distance and the principle of moments.


The Attempt at a Solution


This is where I'm stuck I've reasoned (probably wrongly) that:

(3N x 0.34m) + (y x b) = (z x a)

and y + z = the weight of the ruler.

Where y is the weight of the 350mm long side of the ruler

b is the distance between where the force y is acting (which I'm assuming is just its midpoint) and the pivot

z is the weight of the 650mm side of the ruler.

a is the distance between where the force z is acting (which again I'm assuming is its midpoint) and the pivot.

Not only am I extremely doubtfull that my above formula is correct I can't really see any way that I can determine the weight of the ruler form the information I've been given.
Any help would be greatly appreciated.
 
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  • #2
Where does the 650mm come from? It was not stated in the problem.
 
  • #3
The pivot is at the 350mm mark on the ruler which is 1m long, therefore there are 350mm of ruler before the pivot and 650mm after it.
 
  • #4
If I assume correctly that the total length of the ruler is 650mm, you should sum moments at the fulcrum and set their sum to zero. On one side you have the weight at a certain distance from fulcrum. You also have the ruler weight that would contain the unknown total weight applied to each side of the fulcrum. Since ruler is uniform and you know what proportion is on each side of the fulcrum, you can sum those moments as well. Don't forget the weight of each overhanging side is assumed concentrated at the center of mass which you know because you know where the fulcrum is positioned. The equation you wind up with has one unknown, the weight. Solve for it.
 
  • #5
Our posts overlapped. So the length is 1000mm. Same method applies. Sum moments at fulcrum and equate to zero. Only unknown is weight.
 

1. How do you calculate unknown forces using the principle of moments?

The principle of moments states that the sum of clockwise moments is equal to the sum of counterclockwise moments. To calculate an unknown force, you would need to find the moment arm of the force, which is the perpendicular distance from the axis of rotation to the line of action of the force. Then, you can use the equation M = F x d, where M is the moment, F is the force, and d is the moment arm. By setting the sum of clockwise moments equal to the sum of counterclockwise moments and solving for the unknown force, you can calculate its magnitude.

2. What is the significance of using the principle of moments in force calculations?

The principle of moments is a fundamental concept in mechanics that allows us to analyze the equilibrium of a system. By using this principle, we can determine unknown forces in a system and understand how they contribute to the overall balance of forces. It is often used in engineering and physics to solve problems involving static equilibrium, such as determining the weight of an object on a lever or the tension in a rope.

3. Are there any limitations to using the principle of moments?

While the principle of moments is a powerful tool for calculating unknown forces, there are a few limitations to keep in mind. It assumes that the system is in static equilibrium, meaning that all forces and torques are balanced and there is no net acceleration. It also assumes that the forces are acting purely in the plane of rotation, and any forces acting out of this plane may not be accurately represented in the calculations.

4. How is the principle of moments related to the concept of torque?

Torque is the measure of a force's ability to cause rotational motion around an axis. The principle of moments can be thought of as the rotational equivalent of Newton's Second Law, stating that the sum of forces is equal to mass times acceleration. In the same way, the sum of moments is equal to the moment of inertia times angular acceleration. Both principles are fundamental in understanding the dynamics of a system.

5. Can the principle of moments be applied to non-rigid bodies?

Yes, the principle of moments can be applied to non-rigid bodies as long as they are in static equilibrium. In these cases, the principle is often used to calculate the internal forces and stresses within the body. However, if the body is experiencing any deformations or accelerations, the principle of moments may not accurately represent the system and other methods of analysis may be required.

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