# How to Work With Friction in Kinetic Energy Problems

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The work-energy theorem states that the change in kinetic energy of an object is equal to the work done on that object, but this equation is only valid for frictionless processes. Conservation of energy, in which the sum of the initial kinetic and potential energies is equal to the sum of the final kinetic and potential energy, is technically called the conservation of mechanical energy because it also assumes no friction or air resistance. In the real world, and often in challenging physics problems, friction plays an undeniable role, so it is important to understand how to incorporate friction into kinetic energy problems.

## 2Find the normal force on the object

Find the normal force on the object. If the object is resting on a horizontal surface, the normal force is the same magnitude, or numerical value, as the force of gravity, F=mg, but in the opposite direction as the force of gravity. If the object is on a slanted surface, or other forces are acting on the object, you will have to take components, or directions, into account.

## 3Multiply the normal force by the coefficient of kinetic friction

Multiply the normal force by the coefficient of kinetic friction.

## 4Multiply that product by the distance

Multiply that product by the distance the object moves to find the work done by friction.

## 6If you are using the work-energy theorem

If you are using the work-energy theorem, add the work due to the force of friction to the same side of the equation as the change in kinetic energy.

## 7Are using the conservation

If you are using the conservation of energy equation, add the work due to the force of friction to the same side of the equation as the initial kinetic and potential energies.

## 8Now that you have the complete equation

Now that you have the complete equation, solve for the variable you want.

• The force of friction is a nonconservative force, which is why the work due to the force of friction must be added separately to the work-energy theorem or to the conservation of energy equation.

Allison Boley writes both fiction and nonfiction, having placed as a semifinalist in the international Scriptapalooza Semi-Annual Television Writing Competition. Boley graduated summa cum laude from the Barrett Honors College at Arizona State University, where she is concurrently pursuing her doctorate in physics.