WORK AND CONSERVATIONWORK AND CONSERVATION
OF ENERGYOF ENERGY
AND ALWEN AGYAM
Work is the transfer of energy through motion. In
order for work to take place, a force must be exerted
through a distance. The amount of work done depends
on two things: the amount of force exerted and the
distance over which the force is applied. There are
two factors to keep in mind when deciding when work
is being done: something has to move and the motion
must be in the direction of the applied force. Work
can be calculated by using the following formula:
Work=force x distance
Work is done on the
books when they are
being lifted, but no
work is done on
them when they are
being held or
Work can be positive orWork can be positive or
• Man does positive work
Man does negative work
Gravity does positive work
when box lowers
Gravity does negative work
when box is raised
Work done by a constant ForceWork done by a constant Force
∆Ekin = Wnet
• W = F s = |F| |s| cos θ = Fs s
|F| : magnitude of force
|s| = s : magnitude of displacement
Fs = magnitude of force in
direction of displacement :
Fs = |F| cos θ
θ: angle between displacement and force
• Kinetic energy : Ekin= 1/2 m v2
• Work-Kinetic Energy Theorem:
Conservation of Mechanical EnergyConservation of Mechanical Energy
Total mechanical energy of an object remains constant
provided the net work done by non-conservative forces
Etot = Ekin + Epot = constant
Ekin,f+Epot,f = Ekin,0+Epot,0
Otherwise, in the presence of net work done by
non-conservative forces (e.g. friction):
Wnc = Ekin,f – Ekin,0 + Epot,f-Epot,i
Example ProblemExample Problem
Suppose the initial kinetic and potential energies of a system are 75J
and 250J respectively, and that the final kinetic and potential energies
of the same system are 300J and -25J respectively. How much work
was done on the system by non-conservative forces?
Work done by non-conservative forces equals the
difference between final and initial kinetic energies
plus the difference between the final and initial
gravitational potential energies.
W = (300-75) + ((-25) - 250) = 225 - 275 = -50J.
Samar HathoutSamar Hathout
Conservation of EnergyConservation of Energy
• Gravity, electrical, QCD…
• Friction, air resistance…
Non-conservative forces still conserve energy!
Energy just transfers to thermal energy
PEf + KEf = PEi + KEi
∆KE = −∆PE
A diver of mass m drops from
a board 10.0 m above the
water surface, as in the
Figure. Find his speed 5.00 m
above the water surface.
Neglect air resistance.
A skier slides down the frictionless slope as shown.
What is the skier’s speed at the bottom?
Three identical balls are
thrown from the top of a
building with the same initial
Ball 1 moves horizontally.
Ball 2 moves upward.
Ball 3 moves downward.
Neglecting air resistance,
which ball has the fastest
speed when it hits the ground?
A) Ball 1
B) Ball 2
C) Ball 3
D) All have the same speed.
Springs (Hooke’s Law)Springs (Hooke’s Law)
F = −kx
Potential Energy of SpringPotential Energy of Spring
b) To what height h does the block rise when moving up
A 0.50-kg block rests on a horizontal, frictionless
surface as in the figure; it is pressed against a light
spring having a spring constant of k = 800 N/m, with
an initial compression of 2.0 cm.
Average power is the average rate at which a net force
Pav = Wnet / t
SI unit: [P] = J/s = watt (W)
Or Pav = Fnet s /t = Fnet vav
A 1967 Corvette has a weight of 3020 lbs. The 427
cu-in engine was rated at 435 hp at 5400 rpm.
a) If the engine used all 435 hp at 100% efficiency
during acceleration, what speed would the car attain
after 6 seconds?
b) What is the average acceleration? (in “g”s)
a) 120 mph b) 0.91g
Consider the Corvette (w=3020 lbs) having constant
acceleration of a=0.91g
a) What is the power when v=10 mph?
b) What is the power output when v=100 mph?
a) 73.1 hp b) 732 hp
(in real world a is larger at low v)