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Force parallel to a ramp

A man and a crate

A man needs to load a crate with friction-free wheels and a weight of 1000 N onto the bed of a truck that is 1 m off the ground. He has two differentramps that he can use to push the crate up the ramp and onto the truck.

One ramp is 2.5 m long and the other ramp is 5 m long.

He is able to push the crate up the ramp by pushing in a direction that is parallel to the ramp.


What is the force that he must exert parallel to each ramp to push the crate up the ramp.

Which ramp requires the least amount of work to push the crate up the ramp?

Required force

Trigonometry can be used to compute the amount of force required, parallel to the ramp, to push thecrate up the ramp as a function of the angle that the ramp makes with the horizontal. That force is equal to the product of the weight of the crate (1000N or 225 pound-force) and the sine of the angle that the ramp makes relative to the horizontal.

For example, other than the requirement to overcome inertia to get the crate moving, no force is required to push the crate if the angle is 0 degrees. At theother extreme, if the angle is 90 degrees, the man must lift the crate straight up, bearing the entire weight of the crate. For angles in betweenthese two extremes, the required force is within the capability of one man to achieve.


Ramp #1

  • Truck bed height = 1.0m
  • Ramp length = 2.5m
  • Ramp angle = arcsin(1 / 2.5) = 23.58 degrees
  • Weight of crate = 1000N
  • Component of crate's weight parallel to ramp = 1000 N * sin(23.58 degrees) = 400.03 newtons. This is the force that must be exertedto push the crate up the ramp.
  • Work = (400.03 newtons) * 2.5 meters = 1000.08 joules

Ramp #2

  • Truck bed height = 1.0m
  • Ramp length = 5m
  • Ramp angle = arcsin(1 / 5) = 11.54 degrees
  • Weight of crate = 1000N
  • Component of crate's weight parallel to ramp = 1000 N * sin(11.54 degrees) = 200.05 newtons.This is the force that must be exerted to push the crate up the ramp.
  • Work = (200.05 newtons) * 5 meters = 1000.25 joules

The effect of the ramp

The man only has to exert half as much force to push the crate up Ramp #2 as is required for Ramp #1.

However, he has to push it twice as far with Ramp #2, so the amount of work done on the crate in both cases is 1000 joules.

Like many other simple machines, the use of a ramp (inclined plane) reduces the force required to do a job but it doesn'treduce the amount of work required to do the job.

Do the calculations

I encourage you to repeat the calculations that I have presented in this lesson to confirm that you get the same results. Experiment with the 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: Energy -- Work
  • File: Phy1170.htm
  • Revised: 10/02/15
  • Keywords:
    • physics
    • accessible
    • accessibility
    • blind
    • graph board
    • protractor
    • screen reader
    • refreshable Braille display
    • JavaScript
    • trigonometry
    • work
    • energy
    • power

Financial : Although the openstax CNX site makes it possible for you to download a PDF file for the collection that contains thismodule at no charge, and also makes it possible for you to purchase a pre-printed version of the PDF file, you should beaware that some of the HTML elements in this module may not translate well into PDF.

You also need to know that Prof. Baldwin receives no financial compensation from openstax CNX even if you purchase the PDF version of the collection.

In the past, unknown individuals have copied Prof. Baldwin's modules from cnx.org, converted them to Kindle books, and placed them for sale on Amazon.com showing Prof. Baldwin as the author.Prof. Baldwin neither receives compensation for those sales nor does he know who doesreceive compensation. If you purchase such a book, please be aware that it is a copy of a collection that is freelyavailable on openstax CNX and that it was made and published without the prior knowledge of Prof. Baldwin.

Affiliation : Prof. Baldwin is a professor of Computer Information Technology at Austin Community College in Austin, TX.


Questions & Answers

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 .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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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