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WORK

Work – The product of the magnitudes of the component of
force along the direction of displacement and the
displacement.



Or, more simply, a force that causes a displacement of an object
does work on the object.
Work is done only when components of a force are parallel to a
displacement.
Components of a force perpendicular to a displacement do not do
work.
Net Work Done by a Constant Net Force
Wnet = Fnet d(cos θ)
net work = net force x displacement x cosine of the angle
between them

WORK (CONT.)
Work has dimensions of force times length.
 In the SI system, work has a unit of newtons
times meters (N · m), or joules (J), or
(kg · m2/s2).

 English

or Standard unit of work is the foot · pound.
The joule is named for the British physicist
James Prescott Joule who made major
contributions to the understanding of energy,
heat, and electricity.
WORK (CONT.)

The sign of work is important:
Work is a scalar quantity that can be positive or
negative.
 Work is positive when the component of force is in the
same direction as the displacement.

 Lifting

a box – force is upward, box moves upward.
Work is negative when the force is in the direction
opposite the displacement.
 Sliding
a box – kinetic friction is opposite the displacement of
the box. So kinetic friction does negative work on the box.
POWER

Power – The rate at which work is done or energy is
transferred.


It is possible to do the same amount of work and different
amounts of power.
Power Equation:
P = W/t
power = work ÷ time


The SI unit of power is (J/s) or the watt.
Alternate form of Power
P = Fv
power = force x speed
EXAMPLE PROBLEMS

An appliance salesman pushes a refrigerator 2
meters across the floor by applying a force of 200
N. Find the work done.


Answer: W=Fd(cosθ) = 200N x 2m(cos 0°) = 400 J
A friend’s car is stuck on the ice. You push down
on the car with a 100 N force to provide more
friction for the tires (by way of increasing the
normal force), allowing the car’s tires to propel it 5
meters forward onto less slippery ground. How
much work did you do?

Answer: W=Fd(cosθ) = 100 N x 5 m(cos 90°) = 0 J
EXAMPLE PROBLEMS

Rob and Peter push a couch 5 m across the
floor by applying a 200 N force for 8 seconds.
What power did they supply?
 Answer:
P = W/t = Fd(cosθ)/t = 200 N x 5 m
(cos0°) / 8s = 125 W
ENERGY
Energy – The ability to do work.
 Kinetic Energy – The energy of an object due to its
motion.


Kinetic energy depends on speed and mass.
Kinetic Energy Equation:
KE = ½ mv2
kinetic energy = ½ x mass x (speed)2
 Kinetic energy is a scalar quantity.
 The SI unit of kinetic energy (and all other forms of
energy) is the joule (J).

ENERGY (CONT.)
Work-Kinetic Energy Theorem – The net work
done on an object is equal to the change in the
kinetic energy of the object.
 Work-Kinetic Energy Theorem Equation:
Wnet = ∆KE
net work = change in kinetic energy
 Expanded form:
Wnet = ½ mv2f - ½ mv2i

POTENTIAL ENERGY

Potential Energy – The energy associated with an object
due to the position of the object.


Gravitational potential energy depends on height from a
zero level.
Example: A book on your desk. What is its PE relative to the
floor? What is its PE relative to the desk?
Gravitational Potential Energy Equation:
PEg = mgh
Gravitational potential energy = mass x free-fall
acceleration x height
 PEg depends on both the height and the free-fall
acceleration, neither of which is a property of an object.

ELASTIC POTENTIAL ENERGY

Elastic Potential Energy – The potential energy in a
stretched or compressed elastic object.
Elastic potential energy depends on distance
compressed or stretched.
 The length of a spring when no external forces are
acting on it is called the relaxed length.


Spring Constant – A parameter that expresses how
resistant a spring is to being compressed or
stretched.

It is represented by the symbol k.
ELASTIC POTENTIAL ENERGY (CONT.)
Elastic Potential Energy Equation:
PEelastic = ½ kx2
elastic potential energy = ½ x spring constant x
(distance compressed or stretched)2

CONSERVED QUANTITIES
Mechanical Energy – The sum of the kinetic
energy and all forms of potential energy.
 Mechanical Energy Equation:
MEi = MEf
or

½ mv2i + mghi = ½ mv2f + mghf
MOMENTUM
Momentum – The product of an object’s mass
and the object’s velocity.
 Momentum Equation:
p = mv
momentum = mass x velocity
 The units of momentum are kg • m/s.
 Momentum is a vector quantity.

IMPULSE
Impulse – The product of the constant applied
force and the time interval during which the
force is applied.
 Impulse Equation :
I = Δp = FΔt
Impulse = change in momentum = Force x time
 Units are N•s which equal kg • m/s.

CONSERVATION OF MOMENTUM



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Conservation of Momentum – In the absence of an
external force, the momentum of a system remains
unchanged.
Conservation of Momentum Equation:
m1v1 + m2v2 = m1v1’ + m2v2’
Elastic Collision – In an elastic collision, two objects
return to their original shapes and move away from the
collision separately.
Inelastic Collision – In an inelastic collision, two objects
stick together and move as one mass after the collision.
HOMEWORK
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 Page 171 1-4
 Page 174 1-2
 Page 176 #2
 Page 180 1-3
 Now enjoy your evening!
