Download Energy W = Fd

Energy
There are two basic types of energy:
a) Kinetic - the energy of motion
b) Potential - the energy that is stored
When we consider both of these at the same time it is referred to as Mechanical
energy. However, before we study energy, we must first understand the concept of
work and how it relates to energy.
Work - Work is always done on an object. To do work, a force must be applied to
the object to change its position. Therefore work is quantified by the relationship:
W = Fd
The unit for work is the Joule (J). However if you look at the equation, force (N)
is multiplied to displacement (m).
†
W =N⋅m=J
In Physics, this product is defined as a joule.
Notice also that work is the product of two vectors. This product is a scalar,
†
meaning that work has a magnitude but no direction.
Work is done by individual forces, not Net Force. For example, you can calculate
the work done on a box sliding across the floor by using the applied force or by the
frictional force. Each force does its own amount of work.
There is NO work done on an object under the following conditions:
a) A force is applied to an object but it does not change its position.
b) An objects position changes but no force was applied to it.
c) A force is applied perpendicular to the objects motion
Graphical analysis of force and displacement
F
d
The graph on the left shows a constant force applied over a positive displacement.
The shade area of the graph ( area = length X width) can be used to show The Work
done on this object. ( area = Force X displacement ).
Likewise, the second graph shows the same idea. However, the area formula changes
to reflect the fact that force is now changing over the displacement creating a
triangular area.
How is work related to energy?
Energy has the ability to create a change in an object. This change could involve a
change in an objects velocity or position. To create this change a force needs to be
applied over a distance (Work). Consider the following derivation:
W = Fd
Êv - v ˆ
v
F = ma = mÁ 2 1 ˜ = m 2 (if v 2 = 0)
Ë t ¯
t
Êv + v ˆ v t
d = Á 1 2 ˜t = 2 (if v 2 = 0)
Ë 2 ¯
2
substituting both into the original work formula
W=m
v2 v2t 1
2
= mv 2
t 2 2
In simplest terms, the work done on an object is equal to the quantity
call this the object’s Kinetic Energy.
†
1 2
mv . We
2
Since this object has undergone a change in its kinetic energy,†then the formula that
relates Work and Kinetic Energy is more accurately shown as:
W = DE k
This is known as the Work-Energy Theorem.
†
Gravitational Potential Energy
Gravitational Potential energy is a measure that is dependent upon an object’s
position. Its magnitude is based upon changes in the object’s position. A reference
position must be assigned and all potential energy is compared to this position.
W = DE p = FDd
F = mg, Dd = Dh
DE p = mgDh
As with Kinetic Energy, the units for energy work out to a N ⋅ m or a Joule (J).
Power
†
Its magnitude is directly dependent on
work done and inversely dependent on the time needed to do the work. It is
represented by the formula:
Power is the rate †
at which work is done.
P=
The units for power are
W DE
=
t
t
joules(J)
, which is equivalent to Watts (W).
seconds(s)
† power rating than another object, it simply means that it
If an object has a higher
is able to do more
† work per unit time of the other object. It is more powerful.
Efficiency
A device is able to convert input energy into an intended type of work or output
energy. The ratio between the output energy and the input energy multiplied by 100
quantifies the efficiency of the device.
Eo
¥100 = _______%
Ei
†