Work is only done by a force on an
object if the force causes the object
to move in the direction of the force.
Objects that are at rest may
have many forces acting on them,
but no work is done
if there is no movement.
Work,
by definition, is
the product of the force exerted on
an object and the distance the object
moves in the direction of the force.
W = F·d
Work is a scalar quantity.
The SI unit of work
is the Joule,
named in honor of
James Prescott Joule.
One Joule, J, of work
is the work done when
1.0 N of force is applied
through a distance of 1.0 m.
Graphically, work is
the area under a
“Force vs. Displacement” graph.
displacement, m
If the force and displacement are not
in the exact same direction, then
work = Fd(cosq),
where q is the angle between the force
direction and displacement direction.
F =40 N
35
d = 3.0 m
The work done in moving the block 3.0 m
to the right by the 40 N force at an angle
of 35 to the horizontal is ...
W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J
Energy
the ability (capacity) to do work
Energy comes in many forms:
mechanical, electrical , magnetic, solar,
thermal, chemical, etc...
The SI unit of energy is the Joule.
Energy, like work, is a scalar.
Kinetic Energy
energy of motion
All moving objects that
have mass have kinetic energy.
KE = 1/2
2
mv
m - mass of the object in kg
v - speed of the object in m/s
KE - the kinetic energy in J
Work-Energy Theorem
the net work done on an object is
equal to its change in kinetic energy
Wnet KE
A net force causes
an object to change its KE because
a net force causes an object to accelerate,
and acceleration means a change in velocity,
and if velocity changes, KE changes.
Learn more about the
Work-Energy Theorem
here and here.
Potential Energy
energy of position or condition
gravitational potential energy
PEg = mgh
m - mass of object in kg
g - acceleration of gravity in m/s2
h - height of object, in m,
from some arbitrary reference point
PE – gravitational potential energy in J
Potential Energy
energy of position or condition
elastic potential energy
PEe =
2
½ kx
k – elastic constant in N/m
x - elongation or compression in m
PEe – elastic potential energy in J
Click here to investigate elastic constants.
Law of Conservation of Energy
“Energy can be neither created nor destroyed.
It may only change forms.”
S all types of energy before the event
= S all types of energy after the event
Examples:
•A dropped object loses gravitational PE as it gains KE.
•A block slides across the floor and comes to a stop.
•A compressed spring shoots a ball into the air.
Power,
by definition, is
the time rate of doing work;
or the time rate transfer of energy.
P=W/t
Power is a scalar quantity.
The SI unit of power
is the Watt,
named in honor of
James Watt.
One Watt, W, of power
is the power achieved
when 1.0 J of work is done or
1.0 J of energy is transferred
in a time of 1.0 s.
Simple Machines
“a device that is used to manipulate the amount
and/or direction of force when work is done”
A common misconception is that machines are
used to do a task with less work than would be
needed to do the task without the machine.
They do not! In fact (mainly because of
friction), you actually do more work with a
machine than without it (for the same task).
The major benefit of a machine is that
the work can be done with less applied force,
but at the expense of the distance through
which the force must be applied.
Work = Force x Distance
“large force x
small distance
= small force x large distance”
For example, 1000 J of work is needed
to lift 1000 N onto a table 1.0 m high.
If the object were pushed up a 4.0 m
ramp (inclined plane), a minimum of 250 N
of force would be needed (250 N x 4.0 m
= 1000 J). In reality, friction between
the object and the ramp would make the
necessary force greater than 250 N.
If a 10 m ramp were used, a minimum
of 100 N of force would be needed.
The greater the distance, the
smaller the necessary force.
Efficiency of a Machine
“the ratio of useful work
output to useful work input”
It is impossible to get as much “useful” work
or energy out of a machine as you put into it.
Consider the lever, pulley, and inclined plane as examples
of simple machines:
Inclined plane: decreases
necessary force because
of an increase in distance
Lever: used to decrease
force by increasing distance;
changes direction of force (link)
Pulley: used to decrease force by increasing distance;
may change direction of force (link)
Click here to perform
an interesting activity
on simple machines.
Click here to explore energy, work, and the
Work-Energy Theorem in more depth.