Solve Equilibrium Problem: Painter & Scaffold

In summary, the problem involves finding the reaction forces at the supports of a scaffold with a painter and paint supplies on one end. Using Newton's second law and the concept of rotational equilibrium, the total force acting on the scaffold is calculated to be 1162.485N. From this, the reaction forces at the supports are determined to be 429N and 941N.
  • #1
kee23
17
0

Homework Statement


A 62.5kg painter stands 1.35m from one end of a 45.0 kg scaffold that is 4.50m long. She has 11.0kg supply of paint 1.00m from the end she is nearest to. Find the reaction forces at the supports if the scaffold is supported at each end.

Homework Equations



F=ma
N1+N2-w(mg)=0

The Attempt at a Solution


Well I know that sum of forces equal to zero and the Newton's second law formula F=ma. So I thought of calculating all the weights to get force (N) and then I got stuck. Please help me on this.
 
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  • #2
Hint: Is the system rotating?
 
  • #3
Yes, so the axis of rotation I choose in the left end of scaffold so the right end point will go counter clockwise (+) direction? Also I placed the painter on end of left side of scaffold as well.

http://img404.imageshack.us/img404/7128/equilibrium.png . Here's the diagram I drew.
 
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  • #4
Fpainter= (62.5kg*9.81m/s)= 613.125N
Fsupply= (11.0kg*9.81m/s)= 107.91N
Fstands= 45.0kg*9.81m/s) = 441.45N
Total force Fpainter+Fsupply+Fstands= 1162.485N = N1+N2
Then 613.125N*1.35m+107.91*1.00m/4.50m= N2= 207.9175N
N1+N2= 1132.485N+207.9175N= 1370N
so am I got it right? I don't get it. Please help
 
  • #5
Then 613.125N*1.35m+107.91*1.00m/4.50m= N2= 207.9175N
In this equation you have left one term.
F(stand) acts at the center of the scaffold. So the torque due to this force is
45.0kg*9.81m/s) *2.25m.
Now find N2.
 
  • #6
I got N2 as 429N. Do I add N1(1132.485N)? or subtract to get the other force?

EDIT: Nevermind, I got it. I had the Total force calculation got wrong. Thank you!
 
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FAQ: Solve Equilibrium Problem: Painter & Scaffold

1. How do you determine the equilibrium point for a painter on a scaffold?

The equilibrium point for a painter on a scaffold can be determined by calculating the sum of all the forces acting on the painter and scaffold system. This includes the weight of the painter, the weight of the scaffold, and any external forces such as wind or equipment. The equilibrium point will be where the net force on the system is equal to zero.

2. What factors can affect the equilibrium of a painter on a scaffold?

Several factors can affect the equilibrium of a painter on a scaffold. These include the weight of the painter and scaffold, the location and distribution of the weight on the scaffold, external forces such as wind or equipment, and the stability of the scaffold structure itself.

3. How can you ensure the safety and stability of a scaffold for a painter?

To ensure the safety and stability of a scaffold for a painter, it is important to carefully plan and construct the scaffold according to safety regulations and guidelines. This includes properly securing the scaffold to the building or structure, distributing weight evenly on the scaffold, and regularly inspecting and maintaining the scaffold for any potential hazards.

4. What precautions should a painter take when working on a scaffold?

When working on a scaffold, a painter should always wear appropriate safety gear, such as a hard hat and harness, and follow all safety protocols. They should also be aware of their surroundings and any potential hazards, and make sure the scaffold is stable and secure before beginning work.

5. How can you calculate the weight distribution on a scaffold for multiple painters?

To calculate the weight distribution on a scaffold for multiple painters, you will need to determine the weight of each individual painter, as well as the weight of any equipment or materials they will be using. This information can then be used to calculate the total weight of the system and distribute it evenly on the scaffold to ensure stability and safety.

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