Physics: Finding the Unknown Weight in a Moment Problem

In summary, the beam is in equilibrium when the sum of the weight of the beam and the load is equal to the reaction force on the pivot.
  • #1
seiei
26
0

Homework Statement


A uniform beam of weight 50N is 3.0m long and is supported on a pivot situated 1.0m from one end. When a load of weight W is hung from that end, the beam is in equilibrium. What is the value of W?

I know that the sum of all moments about any given point on an object in equilibrium is equal to zero but I'm not sure how to go about this, any help would be appreciated!
 
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  • #2
Start by identifying the forces acting on the beam. Draw a diagram. Hint: Where does the weight of the beam act?
 
  • #3
Start by drawing a free body diagram of the plank and a pivot point. Put in all the forces and the appropriate distance where it acts.

Hint: Uniform beam means that the weight acts at its geometrical centre.
 
  • #4
At the centre of the beam the weight of 50N acts downwards. That means 1xW=0.5x50 which means W=25N. Is that right?
 
  • #5
seiei said:
At the centre of the beam the weight of 50N acts downwards. That means 1xW=0.5x50 which means W=25N. Is that right?

You forgot a force, the pivot point provides a reaction!

Else your sum of forces in the vertical direction would not balance.
 
  • #6
So the sum of the weight of the beam and the weight of the load = The reaction force? Sorry I'm new to this :(
 
  • #7
seiei said:
So the sum of the weight of the beam and the weight of the load = The reaction force? Sorry I'm new to this :(


Yes that is right. You see on your free body diagram the beam's weight and the load act in the same direction?

For equilibrium, if the sum of the forces in the vertical direction weren't balance then the beam would move down. Agree?
 
  • #8
Yes I see that, thanks! So the weight of the load (25N) and the weight of the beam (50N) are added together to make the reaction force on the pivot (75N)?
 
  • #9
seiei said:
Yes I see that, thanks! So the weight of the load (25N) and the weight of the beam (50N) are added together to make the reaction force on the pivot (75N)?

Yes.


(normally you'd need to be careful where you take your moments in these types of things. Since you took moments about the pivot point, the distance of R from the pivot was 0, so it worked out fine)
 

Related to Physics: Finding the Unknown Weight in a Moment Problem

1. What is a moment in physics?

A moment in physics is a measurement of the turning effect of a force around a point or axis. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the point or axis to the line of action of the force.

2. How is a moment represented in a diagram?

In a diagram, a moment is typically represented by a curved arrow pointing in the direction of the rotation, with the length of the arrow representing the magnitude of the moment. The point or axis around which the moment is being measured is also labeled.

3. What is the difference between a clockwise and counterclockwise moment?

The direction of a moment is determined by the direction of the rotation caused by the force. A clockwise moment causes an object to rotate in a clockwise direction, while a counterclockwise moment causes an object to rotate in a counterclockwise direction.

4. How is the moment of a force calculated?

To calculate the moment of a force, you must first determine the magnitude of the force and the perpendicular distance from the point or axis to the line of action of the force. Then, multiply these two values together to get the moment of the force.

5. What are some real-world applications of moments in physics?

Moments are essential in understanding how objects rotate and move in machines and structures. They are used in engineering to design stable structures, such as bridges and buildings. Moments are also important in sports, such as gymnastics and diving, as athletes use them to perform flips and twists. Additionally, moments are crucial in the study of human anatomy and biomechanics, as they help explain how our bodies move and maintain balance.

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