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WORK – ENERGY - SUMMARY
 Work done by a constant force F exerted on an object through distance d is:
W = Fd cos Ѳ
(Fd = F cos Ѳ)
 Work done by a varying force F - graphically
The area under a Force - distance graph equals
the work done by that force
 Work done by force F is
positive
negative
• when the force and direction of
motion are generally in the
same directions (cos θ = +)
• when the force and direction of
motion are generally in the
opposite directions (cos θ = – )
• the force helps the motion
• force opposes the motion
maximum work
minimum work
W = – Fd
W = Fd
(the work done by friction force is always negative)

Work done by force F is zero if:
• the force is exerted but
no motion is involved:
d = 0, W = 0
• the force is perpendicular to the direction of motion (cos 900 = 0)
for example
work done by normal
force can be zero
normal force is
perpendicular to v
W=0
normal force is
parallel to v
W = Fd = mgh
the work done by centripetal force is zero
Wnet = 0 → Wnet = ∆KE
→ no change in KE
no change in speed;
centripetal force can not
change the speed, only
direction
for example, gravitational
force on the moon does not
change speed of the moon
 Gravitational Potential energy, PE = mgh
What minimum force is needed to lift up an object to height h? F = mg
How much work is done by applied force in lifting it up height h? W = Fd = mgh
That work is now stored as PE in the object: PE = mgh.
So, if a force is lifting up an object along incline or climbing up the stairs, work done by applied force is still mgh.
 Work done by applied force changes potential energy (when net force is zero, so there is no acceleration).
 Work done by net force changes kinetic energy (net force gives acceleration, therefore can change speed).
 Kinetic energy
KE = ½ mv2
 Work – Kinetic energy relationship: work done by net force changes kinetic energy
W = ∆KE = KEf – KEi = ½ mv2 – ½ mu2
W = Fd cos Ѳ
When the net force and direction of motion are in generally the same directions, work is positive and KE is increasing.
When the net force and direction of motion are in generally opposite directions, work is negative and KE is decreasing.
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 Conservation of energy law
For the system that has only mechanical energy (ME = PE + KE)
and there is no frictional force acting on it, so no mechanical energy
is converted into heat, mechanical energy is conserved
ME1 = ME2 = ME3 = ME4
mgh1 + ½ mv12 = mgh2 + ½ mv22 = • • • • • •
 Conservation of energy law with friction included
Friction converts part of kinetic energy of the object into heat energy. We say that the frictional force has dissipated energy.
This energy equals to the work done by the friction and it doesn’t belong to the object alone but is shared with environment.
ME1 – Ffr d = ME2
(Wfr = – Ffr d)
P=
 Power is the work done in unit time or energy converted in unit time 𝑷 =
𝑾
𝒕
or 𝑷 =
𝑬
𝒕
measures how fast work is done or how quickly energy is converted. Power is a scalar quantity.
Units: 1 W(Watt) = 1 J/ 1s

There is another way to calculate power P = F v
W
t
or P =
E
t