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Forces along an Incline: Applied Forces, Normal Forces, and Frictional Forces – A Vector Based Problem Solver, Calculator, & Component Resolver

Learning Tool Last Enhanced on February 2, 2013 at 3:51 am by admin — 7 Comments ↓

Free body force diagrams are used to show that objects on an incline are subject to forces resulting from gravity and friction.

This tool can be used to determine the forces acting on an object on an incline. Given the mass of an object, it will find the following forces (in Newtons):

  1. Force due to gravity (weight) of an object
  2. The Normal force (the perpendicular force from that the inclined surface exerts on the object)
  3. The corresponding force component along the incline (downhill force due to gravity)
  4. Any frictional forces (due to static friction or kinetic friction, if applicable) along the incline
  5. The applied force required to prevent the object from sliding, or necessary to pull uphill at a constant speed

The calculator will not only depict the mathematical steps involved to compute the answer, but will also display a labeled free body force diagram. All answers are provided to three decimal places. (These tools only support integers and decimals, fractions are not allowed)

*A javascript-enabled browser is required to use this tool.

Calculate and Resolve Forces Exerted by Gravity on an Object on a Ramp: Applied, Normal, and Frictional Forces

Calculate Forces for Object on an Incline, given mass and angle of inclination
Angles should be input in degrees, measured counterclockwise from the horizontal axis / 0 degrees / East.
Acceleration due to Gravity to be used in calculation (m/s2)
Mass of Object (kg) Angle of Inclination (degrees)
Coefficients of Friction (if applicable)
Coefficient of Static Friction (μs) Coefficient of Kinetic Friction (μk)
If kinetic friction exists:
  • Paul

    Should add the functionality for multiple adjacent boxes since the internal forces will be different and same with the normal forces.

  • Ian

    You made an error with the coefficient of friction calculations. Mu(s) should not be the same as Mu(k). Therefore, Fstatic and Fkinetic should yield different values.

  • Kate Midgley

    Sorry I have a potentially dumb question to ask. In an inclined plane question like this, does an applied force going up the ramp (either pushing or pulling) affect the Force Normal?

    • http://www.getfitcanada.org Jeffrey Vdovjak

      I’m answering this here, because someone might have the same question (as I did). In this case… no, the applied force is not going to affect the force normal because the applied force is in alignment with the slope.

      In order to solve this problem, you use normal and tangental axes, which is your “new x and y”. The tangental axis (which is your “new x”) is parallel to the slope. Therefore, the applied force, because it runs parallel to the slope, is completely in your “x” axis, and does not affect the force normal (which is completely in your “new y axis”).

      In this case, where force applied is aligned with the slope, it is perpendicular to the force normal and therefore does not affect it. I had the same thought, and had to reason out why the answer here was correct.

  • 1goodamerican

    I understand there is a friction factor in each calculation though if the object is being pushed or pulled on rollers on a 10 degree plane and the weight is constant 180 lbs, can this be calculated into a ratio equaling the lbs (not force) it would take to move it up hill example it takes 30 % force of the weight to move the object equaling 300 newtons = 60 lbs (this is false numbers only used as an example)

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  • Jim

    This is one of the most useful websites on the internet