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For horizontal equilibrium

F4 = F2 = 26133 newtons

For vertical equilibrium

F3 = F1 = M*g = 2000kg*9.8m/s^2, or

F3 = 19600 newtons

The magnitude of the force = sqrt(F4^2 + F3^2), or

Magnitude = sqrt(26133^2 + 19600^2), or

Magnitude = 32666 newtons

Therefore, the magnitude of the force is 32666 newtons.

The angle of the force is

angle = atan(19600 newtons/26133 newtons) in degrees

angle = 36.9 degrees north of east

A ladder scenario

A ladder is sitting on a horizontal floor and leaning against a smooth wall. A bucket of paint is hanging from a rung 80-percent up from the bottom of theladder. The parameters are as follows:

  • Length of ladder = L = 5 m
  • Angle between ladder and floor = A = 50 degrees
  • Mass of the bucket of paint = m = 2.5 kg
  • Mass of the ladder = M = 12 kg
  • Coefficient of static friction = u = ?

Part 1

Draw a vector diagram of the forces acting on the ladder.


There are five forces acting on the ladder:

  1. A force directed outward from the wall at the top of the ladder. Label this force F1.
  2. A force pushing straight down due to the mass of the bucket of paint. Label this force F2.
  3. A force pushing straight down due to the mass of the ladder. Label this force F3.
  4. A force at the bottom of the ladder directed toward the wall due to static friction. Label this force F4.
  5. A force at the bottom of the ladder directed straight up due to the weight of the ladder and the bucket of paint. Label this force F5.

Part 2

The ladder is in static equilibrium.

The coefficient of static friction between the ladder and the wall is zero.

What is the minimum possible value for the coefficient of static friction between the ladder and the floor.

F1 = ?

F2 = m*g = 2.5kg * 9.8m/s^2 = 24.5 newtons

F3 = M*g = 12kg*9.8m/s^2 = 117.6 newtons

F4 = F5*u

For vertical equilibrium,

F5 = F2 + F3 = (2.5kg + 12kg)*9.8m/s^2 = 142 newtons

For rotational equilibrium, the sum of the torques about the bottom of the ladder must be zero.

Compute the horizontal distance to the line of action of the weight of the ladder.

X1 = (L/2)*cos(50 degrees), or

X1 = ((5/2)m)*cos(50 degrees), or

X1 = 1.61m

Compute the horizontal distance to the line of action of the weight of the bucket of paint.

X2 = 0.8*5m*cos(50 degrees), or

X2 = 2.57m

Compute the vertical distance to the line of action of the horizontal force at the top of the ladder.

Y1 = 5m*sin(50 degrees), or

Y1 = 3.83m

Compute sum of the torques about the bottom of the ladder.

Y1*F1 - X2*F2 - X1*F3 = 0, or

F1 = (X2*F2 + X1*F3)/Y1, or

F1 = (2.57m*24.5 newtons+ 1.61m*117.6 newtons)/3.83m

F1 = 65.87 newtons

For horizontal equilibrium,

F4 = 65.87 newtons

By substitution,

F4 = F5*u = 65.87 newtons

u = (65.87 newtons)/F5, or

u = (65.87 newtons)/142 newtons, or

u = 0.46

While the coefficient of static friction could be higher than this and still achieve static equilibrium, if the coefficient were any lower, the ladder wouldslide away from the wall.

Repeat the computations

I encourage you to repeat the computations that I have presented in this lesson to confirm that you get the same results. Experiment withthe scenarios, making changes, and observing the results of your changes. Make certain that you can explain why your changes behave as they do.


I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.


This section contains a variety of miscellaneous information.

Housekeeping material
  • Module name: Angular Momentum -- Rotational equilibrium
  • File: Phy1340.htm
  • Revised: 10/02/15
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • rotational equilibrium
    • translational equilibrium
    • static equilibrium
    • beam
    • boom
    • crane
    • crate
    • ladder

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Questions & Answers

are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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