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Question

A wheel has been described as one of the greatest invention of man. Why?


Solution

wheels - one of the greatest invention of man

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.

wheel1.gif (5383 bytes)

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?

  • 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 forklift lifts the car so that the wheels do not touch the ground and you get in the car, start the engine, put it into "drive", and step on the accelerator, then the wheels start turning.  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 icy surface or your car is stuck in mud, the wheels will turn, but your car does not accelerate.  The center of mass of a system acted on only by internal forces cannot accelerate.  This is a consequence of Newton's third law.  We need an external force to accelerate the car, and that force is friction.

How does friction accelerate your car?

pwheel.gif (3472 bytes)

  • 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 the frictional force on the portion of the wheel contacting the ground is opposite to the direction 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 wheel is accelerating, internal forces try to accelerate the contact point backward.  The force 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 the car in the horizontal direction, and without it there would be no net force to accelerate the car.
  • How can the force of static friction be responsible for accelerating the car and do no work?  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 can cancel one of the forces of an action-reaction pair with a direction opposite to the direction of the acceleration, leaving a net force in the direction of the acceleration.


 

 wheel is an important invention. Without it, things would be really different.

Wheels can be used for transportation. For example, before the wheel was invented, people had to walk, carry very heavy things, and had to use a boat to get over seas. Now we have cars, bicycles, wagons, dollies and airplanes!

First of all, wheels can get you from place to place. The wheel started out as a simple invention. For example, dollies help humans carry very heavy things just by tilting them back on their wheels. Also, disabled people who can’t walk, rely on wheelchairs.

We rely on wheels for transportation and carrying things. Without wheels e would be walking to our destination. Wheels are on cars and airplanes and a lot of other things. That’s why I think the wheel is the most important invention. Also, you can’t go one day without seeing a wheel.


Physics

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