Work and Energy 

When a force moves in the direction along which it acts, work is done by that
force. 



So, one might ask the question... what exactly is work? 



Work is the process of converting energy from one form to another
(electrical energy to thermal energy, chemical energy to kinetic energy etc) 



OK, so, what exactly is energy? 



Well... energy is what you need if you want to do work...! 

(Slightly more
formal sounding statement: Energy is the ability to do work.) 



If these two interdependent definitions seem less than satisfactory, look
at it from a "practical" point of view. Do we know what we mean by energy? 



Yes;
energy is the useful thing we get from electricity, chemical reactions like burning,
motive force from the the wind (kinetic energy), potential for water stored
behind a dam to give us electricity (gravitational potential energy)
etc 



In other words, the two terms, work done and energy converted,
mean exactly the same thing. 

The quantity of work done (or energy converted) by a force, when the
force moves, depends on two obvious factors:  the distance moved (in the direction along which the force
acts) and  the magnitude (strength) of the force 



To convince yourself of this, consider first climbing up 20 stairs and then later
climbing up 200 stairs; in which case are you more tired? 

Greater distance; you will be more tired. 

Similarly, consider first climbing up those stairs
carrying nothing and then climbing up those same stairs carrying a
50kg sack of potatoes* on your back. 

Bigger force needed; again, more tiring. 



We use this idea to define the quantity of work done in a given situation by the
following equation: 

work done = force × distance moved in the direction of the force 



note that, although both force and displacement (distance moved in a
specified direction) are vector quantities, work (energy) is a scalar
quantity. The above equation is said to represent a scalar product
of two vectors. 



The equation above also leads us to a unit for measuring quantities of work, the
Newtonmetre. 



However, in honour of a scientist who did a lot of work on work (sorry about
that), James Prescott Joule (1818  1889), 1Newtonmetre
is called 1Joule 



1Joule is the quantity of work done when a
force of 1N moves a direction of
1m along its own line of action. 


If the direction of the displacement is not the same as the direction of
the force, we use the component of the force which is parallel to the
displacement. 



For example, when a body is caused to accelerate down an
inclined plane by the force of gravity, as shown here. 



The magnitude of
the component of the force of gravity acting parallel to the displacement is
given by the magnitude of the force multiplied by the cosine of the
angle between the force and the displacement. 



We can therefore state the more general equation: 



One of the most useful facts about energy is that the total amount of energy in
the universe is thought to be constant. 

This idea is expressed in the law of conservation of energy: 

The energy in any closed system is never lost but can be changed from one form
to another. 



This law can help us simplify many calculations/predictions in physics, click
here for an example. 



Examples of energy conversions: 

 A battery converts chemical energy into electrical energy 

 An electric motor lifting an elevator converts
electrical energy into
gravitational potential energy 

 A nuclear reactor converts nuclear energy into thermal energy. 

 When a moving vehicle uses its brakes to stop, the kinetic energy
of the vehicle is converted to thermal energy in the brakes. 

(This
is an interesting case because thermal energy is just kinetic energy but
possessed by many randomly moving particles...) 



Power 

Consider two car motors. 

One might be described as being more powerful
than the other. 

Both motors are capable of
doing the same amount of work but the
more powerful motor can do the work more quickly. 

This consideration leads us to
the following definition of the word power: 

Power is the rate of doing work (or converting energy) or 

Power is the work done (or energy converted) per unit time 



the unit of power is therefore the Joule per second, Js^{1}


However, a power of 1Js^{1} is called 1Watt (1W) after James Watt an
18^{th} century mechanical engineer who did work on steam engines. 



Combining this equation with the definition of work we obtain another useful
equation: 



Click here for power calculation example 





*ok, so it doesn't specifically have to be
potatoes... you get the point! 
