The force of static friction does no work and you do no work against this force. Eventhough you may be pushing hard against an object acted on by the force of static friction,the object is not moving. The displacement is zero and W = 0.

You, however, do work against the force of sliding friction. If you push with force F ona cabinet, while the cabinet moves with constant velocity through a distance d in thedirection of F, the work you do on the cabinet is W = Fd = mNd. The force of fiction doesnegative work W = -mNd on the cabinet.

Work is the conversion of one form of energy into another. You do positive work on thecabinet, but the cabinet is not gaining potential energy, (it is not being pushed up a hill),and it is not gaining kinetic energy (it is moving with constant speed). The work done bythe frictional force (negative work) on the cabinet transforms the energy you transfer tothe object into disordered energy.

Sliding friction converts most of the work you do on the file cabinet into thermal energy. As you slide the cabinet across the floor, the bottom of the cabinet and the floor getwarmer. This thermal energy cannot easily be converted back into ordered energy, itcannot easily be used to do useful work.

Sliding friction also causes wear. Some of the work you do on the file cabinet isconverted into electrostatic potential energy. The atoms and molecules in a solid objectare held together by electrical forces, and you have to do work to break them apart. Todetach a cluster of atoms from the bottom of the file cabinet you must do work againstthe electrostatic force, in the same way you must do work against the gravitational forceto lift a rock up from the ground. As you slide your cabinet across the floor, somematerial is removed from the bottom of the cabinet and from the floor. It will not takelong before damage becomes visible.

Rolling

If you put your file cabinet on a small cart with wheels, you can greatly reduce the forceyou need to apply to move the cabinet with constant speed. Wheels do not slide acrossthe floor, they roll across the floor. At any instant only a very small portion of thesurface of a wheel is in contact with the floor. If you push on the cart, static frictionprevents this portion from sliding. As the wheel rolls, a new portion of the wheel islowered onto the floor, while the portion previously in contact with the floor is raised. Pure rolling involves only static friction, not kinetic friction.

A cart on wheels can roll across the floor. Rolling involves only static friction, not slidingfriction. Static friction does no work. Rolling does not involve the production of thermalenergy. However, to attach two wheels to the cart, you need an axle. A smooth bearinglets the axle slide inside the hub of the wheel. The force of sliding friction converts someof the kinetic energy into heat, and exerts a torque on the wheel. However, the surfacesof the bearing are usually very smooth and the hub has a small radius, so that the totalamount of work done against frictional forces is small. Adequate lubrication can reduce iteven further.

In the diagram above the force of static friction prevents the contact point between wheeland ground from slipping as the applied force accelerates the cart. The applied force doespositive work and the cart gains kinetic energy.

Powering Wheels

You get in your car, start the engine, put it into "drive", step on the accelerator, andaccelerate. What makes the car start moving forward?

Let us, for the moment, forget about the details of the engine and the transmission. The car contains all the hardware necessary to make the wheels turn. If a forkliftlifts the car so that the wheels do not touch the ground and you get in the car, startthe engine, put it into "drive", and step on the accelerator, then the wheels startturning. The car, however, does not start moving forward.

What is missing?

Without frictional forces your car will not accelerate. If you are parked on an icysurface or your car is stuck in mud, the wheels will turn, but your car does notaccelerate. The center of mass of a system acted on only by internal forces cannotaccelerate. This is a consequence of Newton's third law. We need an external forceto accelerate the car, and that force is friction.

How does friction accelerate your car?

Assume you want the car to accelerate towards the right. When a wheel is spinning,the contact point with the ground is moving towards the left. The direction of thefrictional force on the portion of the wheel contacting the ground is opposite to thedirection of the velocity of this portion of the wheel with respect to the ground. When a wheel is rolling the contact point is not sliding at all. When a rolling wheelis accelerating, internal forces try to accelerate the contact point backward. Theforce of static friction now is directed towards the right and it cancels those forces. Neglecting drag, the force of static friction is the only external force acting on thecar in the horizontal direction, and without it there would be no net force toaccelerate the car.How can the force of static friction be responsible for accelerating the car and do nowork? Internal forces between different parts of the car in the engine, transmission,etc, come in action-reaction pairs. These forces can do work. The frictional force cancancel one of the forces of an action-reaction pair with a direction opposite to thedirection of the acceleration, leaving a net force in the direction of the acceleration.