Choose a solve mode for kinetic work or its energy-loss magnitude from normal force, coefficient and distance, including flat and inclined surfaces. The static option reports a limiting force × distance scale, not actual static work.

Kinetic model assumes sliding on a fixed surface. Static option gives a maximum force × distance scale, not actual static work.

Model settings and presets

Approximate reference values; actual surfaces and conditions vary.

Work Done By Friction Formula

For an object sliding on a stationary surface, kinetic friction does negative work. The positive magnitude is the energy dissipated or work done against friction.

Wf = - NF × u × D
  • Where Wf is signed work by kinetic friction (J or N·m); its nonnegative magnitude E = −Wf
  • NF is the normal force (N) 
  • u is the kinetic coefficient of friction 
  • D is the distance (m) 

Multiply normal force by the kinetic coefficient and distance along the surface to obtain the energy-loss magnitude E. Work on the sliding object is Wf = −E. On a flat surface N = mg; on an incline N = mg cos(θ), assuming no additional perpendicular force. For inverse modes enter nonnegative E. Static friction obeys |f| ≤ μsN; the static option uses the maximum force to calculate a reference scale, not actual static work.

How to Calculate Work Done By Friction?

The following example problems outline how to calculate the Work Done By Friction.

Example Problem #1

  1. First, determine the normal force (N). In this example, the normal force (N) is given as 150.
  2. Next, determine the coefficient of friction. For this problem, the coefficient of friction is given as  .75.
  3. Next, determine the distance (m). In this case, the distance (m) is found to be 30.
  4. Finally, calculate the Work Done By Friction using the formula above: 

Wf = −NF * u * D

Inserting the values from above and solving yields: 

Wf = −150 × 0.75 × 30 = −3375 J; energy dissipated E = 3375 J

FAQ

What is the significance of the coefficient of friction in calculating work done by friction?

The coefficient of friction is a dimensionless scalar value that represents the ratio of the force of friction between two bodies and the force pressing them together. It plays a crucial role in calculating work done by friction because it quantifies how much frictional force is generated for a given normal force. For kinetic sliding, a higher coefficient increases the magnitude of negative friction work. For static friction, μsN is only an upper force limit.

How does the normal force affect the work done by friction?

The normal force, which is perpendicular to the contact surface between two objects, directly influences the work done by friction. Since the frictional force is proportional to the normal force (multiplied by the coefficient of friction), an increase in the normal force results in a higher frictional force. Consequently, for a given distance and coefficient of friction, a larger normal force increases the magnitude of negative kinetic-friction work.

Can the work done by friction be negative, and what would that imply?

Work is negative when friction opposes displacement and positive when friction acts along displacement. This calculator models kinetic sliding on a stationary surface, so Wf = −μkND. A moving conveyor can do positive friction work on an object in the ground frame; that situation requires a different motion model. Static friction is not generally μsN, and its actual work cannot be inferred from μs alone.