Mechanical Work and Power:
Learning Goal
The student will use appropriate terminology
related to energy including work, gravitational
potential energy, kinetic energy, and power; and
perform calculations related to the work done in
a mechanical system.
Mechanical Work and Power
SPH4C
Mechanical Work: a Definition
The mechanical work on an object is the amount
of mechanical energy transferred to that object
by a force.
Mechanical Work: a Definition
The mechanical work on an object is the amount
of mechanical energy transferred to that object
by a force.
W  E
Mechanical Energy: a definition
The mechanical energy of an object is that part of
its total energy which is subject to change by
mechanical work.
(definition by the Department of Redundancy Department)
Mechanical Energy: a definition
The mechanical energy of an object is that part of
its total energy which is subject to change by
mechanical work.
(definition by the Department of Redundancy Department)
Energy is a concept so fundamental in physics that
it is not easily defined in terms of anything more
fundamental.
Mechanical Energy: a definition
The mechanical energy of an object is that part of
its total energy which is subject to change by
mechanical work.
(definition by the Department of Redundancy Department)
It is easier just to understand energy in terms of its
component kinetic and potential energies.
Mechanical Energy: a definition
Kinetic energy is the energy of motion and
potential energy is the energy to, potentially, do
something else.
Energy: example
Thermal energy, the energy of the
particles of a substance, is partly
kinetic energy and partly potential
energy:
Energy: example
Thermal energy, the energy of the
particles of a substance, is partly
kinetic energy and partly potential
energy:
The kinetic energy is in the kinetic
energy of the atoms.
Energy: example
Thermal energy, the energy of the
particles of a substance, is partly
kinetic energy and partly potential
energy:
The kinetic energy is in the kinetic
energy of the atoms.
The potential energy is stored in the
deformation of atomic bonds during
this motion.
Energy: Units
The SI derived unit of work is the Joule:
Energy: Units
The SI derived unit of work is the Joule:
1J  1
kg m
s2
2
Energy: more units
But there exist other metric units, e.g.
1kWh  36
.  10 J
6
Energy: more units
But there exist other metric units, e.g.
1kWh  36
.  10 J
6
1cal  4.184 J
Calories
A calorie is the amount of heat necessary to raise
the temperature of 1 g of water by 1oC (at
standard atmospheric pressure).
Calories
A calorie is the amount of heat necessary to raise
the temperature of 1 g of water by 1oC (at
standard atmospheric pressure).
Food energy is measured in kilocalories
(or Calories with a capital C).
1Cal  1  10 cal  4184
.
 10 J
3
3
Back to Work
In the simplest case of an object moving in one
direction and a constant force applied parallel to
that direction:
Back to Work
In the simplest case of an object moving in one
direction and a constant force applied parallel to
that direction:
W  Fd
Where F is the magnitude of the applied force and
d is the distance the object travels. Note that
work is a scalar quantity.
Work: example 1
Ms. Rosebery applies a horizontal force of
magnitude 40.0 N to push a 10.0 kg box 15.0 m
across a frictionless surface. Find the work done
on the box.
Work: example 1
Ms. Rosebery applies a horizontal force of
magnitude 40.0 N to push a 10.0 kg box 15.0 m
across a frictionless surface. Find the work done
on the box.
W?
F  40.0 N
d  15.0 m
Work: example 1
Ms. Rosebery applies a horizontal force of
magnitude 40.0 N to push a 10.0 kg box 15.0 m
across a frictionless surface. Find the work done
on the box.
W?
W  Fd
F  40.0 N
W  (40.0 N )(15.0 m)
d  15.0 m
Work: example 1
Ms. Rosebery applies a horizontal force of
magnitude 40.0 N to push a 10.0 kg box 15.0 m
across a frictionless surface. Find the work done
on the box.
W?
W  Fd
F  40.0 N
W  (40.0 N )(15.0 m)
d  15.0 m W  6.00  102 J
Work: example 2
Ms. Rosebery applies a vertical force of magnitude
40.0 N on a 10.0 kg box as it slides 15.0 m
across a frictionless surface. Find the work done
on the box.
Work: example 2
Ms. Rosebery applies a vertical force of magnitude
40.0 N on a 10.0 kg box as it slides 15.0 m
across a frictionless surface. Find the work done
on the box.
W 0
Work: example 2
Ms. Rosebery applies a vertical force of magnitude
40.0 N on a 10.0 kg box as it slides 15.0 m
across a frictionless surface. Find the work done
on the box.
W 0
Ms. Rosebery is not increasing the speed of the
box and thus its mechanical energy. Forces
applied at right angles to the motion don’t count.
Work done by friction
If there is a frictional force, it will do negative work
on the object, i.e. reduce its total mechanical
energy.
Work: Example 3
Ms. Rosebery applies a horizontal force of magnitude
40.0 N to push a 10.0 kg box 15.0 m across a surface.
The frictional force is 10.0 N. Find the work done by
friction on the box.
Work: Example 3
Ms. Rosebery applies a horizontal force of magnitude
40.0 N to push a 10.0 kg box 15.0 m across a surface.
The frictional force is 10.0 N. Find the work done by
friction on the box.
W  Fd
W  (10.0 N )(15.0 m)
W  1.5010 J
2
Remember that friction is
opposite the direction of
motion.
Work: Example 3
The total change in energy of the box would be:
E  WRosebery  W friction
E  6.0010 J  1.5010 J
2
2
E  4.50102 J
The work done by friction would have gone into creating
heat and sound energy.
Power
Power is the rate at which work is performed or
energy is transferred:
W
P
t
Power
Power is the rate at which work is performed or
energy is transferred:
W
P
t
It has units of J/s or Watts (W).
Power
Power is the rate at which work is performed or
energy is transferred:
W
P
t
It has units of J/s or Watts (W).
More Practice
Mechanical Work and Power Lab Activity