Statics: Balancing beam of unknown length

In summary, the problem involves a horizontal meter stick with a mass of 217 g and three weights placed at various locations on the stick. The goal is to determine at what location the system would be in balance if suspended there. This requires the net force and torque on the system to be equal to zero. The equation for the center of mass in the x-dimension is also relevant.
  • #1
togg
3
0

Homework Statement


A horizontal meter stick has a mass of 217 g. Three weights ride on the meter stick: 265 g at 40.7 cm, 191 g at 75.9 cm, and 195 g at 99.3 cm. At what location on the meter stick would the system be in balance if it were suspended there?

Homework Equations


ƩF=0
Ʃτ=0
Center of mass (x-dimension) = (M1X1 +M2X2...)/(M1+M2...)

The Attempt at a Solution


I know that in order for the system to balance the torque on the system as well as the net force must both equal zero. I have just begun this section and I am not really sure how to approach this problem. Thank you for your time.
 
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  • #2
Your post topic says "Statics: Balancing beam of unknown length".
The problem statement says, "A horizontal meter stick ..."

I don't know how long your meter stick is, but all of mine are 1 meter long.
 
  • #3
You were correct. That was a simple mistake, thank you for the help.
 

1. What is statics and why is it important?

Statics is a branch of physics that deals with the study of objects at rest or in equilibrium. It is important because it helps us understand the forces acting on a system and how to balance those forces to keep an object or structure at rest.

2. How do I find the length of a balancing beam?

In order to find the length of a balancing beam, you must set up an equation that represents the forces acting on the beam. This equation will include the weight of the beam, the weight of any objects on the beam, and the reaction forces at each end of the beam. Solving this equation will give you the length of the beam.

3. What is the difference between a static and dynamic balancing beam?

A static balancing beam is one that is at rest and in equilibrium, meaning all forces acting on it are balanced. A dynamic balancing beam is one that is in motion, with forces acting on it that are changing over time. The principles of statics can still be applied to a dynamic balancing beam, but additional factors must be considered.

4. Can a balancing beam of unknown length be balanced?

Yes, a balancing beam of unknown length can be balanced. This can be achieved by setting up an equation that represents the forces acting on the beam and solving for the unknown length. It is important to note that the unknown length must be within a reasonable range for the beam to be balanced.

5. What are the consequences of an unbalanced balancing beam?

If a balancing beam is unbalanced, it may tip over or collapse, causing damage or injury. It is important to ensure that all forces acting on the beam are balanced to prevent any potential hazards.

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