Wheels

Up Frictional Forces Kinetic Energy Power Wheels

The force of static friction does no work and you do no work against this force.  Even though 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 on a cabinet, while the cabinet moves with constant velocity through a distance d in the direction of F, the work you do on the cabinet is W = Fd = mNd.  The force of fiction does negative work W = -mNd on the cabinet.

Work is the conversion of one form of energy into another.  You do positive work on the cabinet, 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 by the frictional force (negative work) on the cabinet transforms the energy you transfer to the 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 get warmer.  This thermal energy cannot easily be converted back into ordered energy, it cannot easily be used to do useful work.

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


Rolling

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

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

In the diagram above the force of static friction prevents the contact point between wheel and ground from slipping as the applied force accelerates the cart.  The applied force does positive 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, and accelerate.
What makes the car start moving forward?

What is missing?

How does friction accelerate your car?

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