Transcript Chapter 5 Work and Energy

Section 5-1
Work – Section 5-1
Definition of Work

Ordinary Definition : To us, WORK means to do
something that takes physical or mental effort.
◦ Ex: Holding a Chair at Arm’s Length for several Minutes

Scientific Definition : In Physics, WORK is ONLY done
when a force causes an object to be displaced (move).
Ex : Pushing a chair from one side of the room to
the other.

There are three key words in this definition - force,
displacement, and cause. In order for a force to qualify as
having done work on an object, there must be a
displacement and the force must cause the displacement.

Work is done ONLY when components of
a force are parallel to or at an angle (not
90 degrees) to the displacement.
Ex: Push Chair Horizontally, only horizontal
component of force

Components of the force perpendicular to
a displacement do NOT do work.
 Ex: If you are exerting force to move an object
horizontally, vertical force will not do work on
the object.
Work Formula

W = Fd(cos angle)

Work = Force x displacement x cosine of
angle between them.

If angle = 0 degrees, cosine of 0 degrees = 1
so we can use W = Fd

If angle = 90 degrees, cosine of 90 degrees =
0 and W = 0.
◦ No work is done on a bucket of water being carried
by a student walking horizontally. (Upward force is
perpendicular to the displacement of the bucket).
Example

Let's consider the force of a
chain pulling upwards and
rightwards upon Fido in order to
drag Fido to the right.

It is only the horizontal
component of the tensional
force in the chain which causes
Fido to be displaced to the right.

The horizontal component is
found by multiplying the force F
by the cosine of the angle
between F and d. In this sense,
the cosine theta in the work
equation relates to the cause
factor - it selects the portion of
the force which actually causes
a displacement.
Example



Since F and d were in
the same direction, the
angle was 0 degrees.
Nonetheless, most
students experienced
the strong temptation to
measure the angle of
incline and use it in the
equation.
Don't forget: the angle
in the equation is not
just any angle; it is
defined as the angle
between the force and
the displacement
vector.
Units of Work

Work has dimensions of Force and
Length.

In SI system, work has a unit of newtons
times meters (N*m) or Joules (J).
ex: Work done lifting an apple from your
waist to
the top of your head is about 1 J.
Three push ups require about 1,000
J.
The sign of work is Important.

Work is a scalar quantity.

Work can be positive or negative.

Work is positive when the component force is in
the same direction of displacement.
 Ex: when you lift a box, work done is positive because
the force is upward and the box is moving upward.

Work is negative when the force is in the
direction opposite the displacement.
 Ex: Force of kinetic friction between sliding box and the
floor is opposite the displacement of the box.
Guided Practice

Pg. 169 Sample 5A
Section 2 Energy
Kinetic Energy
Work-Kinetic Energy Theorem
Different forms of Energy

Energy has a number of different forms, all
of which measure the ability of an object or
system to do work on another object or
system.

In Chapter 5 we will learn about the following
types of energy:
- Kinetic Energy
- Potential Energy
- Gravitational Potential Energy
- Elastic Potential Energy
- Mechanical Energy
Kinetic Energy (KE) :

Energy associated with an object in
motion.

Scalar quantity.

SI unit = (J) Joule (same unit for work).

Depends on speed and mass.
Formula for Kinetic Energy
 KE
= ½ m v2
 Kinetic
Energy = ½ x mass x
(speed)2
 Kinetic
Energy depends on BOTH
an object’s speed and mass.
Let’s Practice some problems…

Open your books to pg. 173 and work
sample problem 5B
Work-Kinetic Energy Theorem

Net work done by a Net Force acting on
an object is equal to the change in the
kinetic energy of the object.

Net work = change in kinetic energy
= Δ KE
 Wnet = KEf - KEi
 Fnet d(cos θ) = ½ mv2f – ½
mv2i
 Wnet
Fnet

In these problems, Fnet means the net
force doing the work.

Using our Work-Kinetic Energy Theorem
our Fnet can
mean :
○ Friction Force (Remember Ff = μFn )
○ Constant Force
○ Forward Force Minus Resistive force
Section 3
Conservation of
Mechanical Energy
Conservation of Energy

Energy can never be lost. It can only change form.
Energy is a conserved quantity.

When something is conserved, it remains
constant.

The form of a conserved quantity can change, but
we will always have the same amount.

Mass is an example of a conserved quantity.
Conserved Quantity

The mass of the light bulb whether whole or
in pieces is constant and thus conserved.
Mechanical Energy

Can be either kinetic energy (energy of
motion) or potential energy (stored energy of
position).

Is the sum of kinetic energy and all forms of
potential energy of an object or group.

Is not conserved in the presence of friction.
Mechanical Energy

Is conserved only in the absence of friction.

When there is no friction, mechanical
energy can be conserved.

This principle is called Conservation of
Mechanical Energy:
 MEi = MEf
 Initial Mechanical Energy = Final Mechanical
Energy
Mechanical Energy

Formula :
 MEi = MEf
 MEi = PEi + Kei
 MEf = PEf + Kef
 Therefore :
 PEi + KEi = PEf + KEf
Practice Problem

Pg. 184 Sample Problem 5E
Section 4
Power
Power

The rate at which work is done.

Rate of energy transfer by any method.

Machines with different power ratings do the
same work in different time intervals.

The more power you have, the faster your
work will get done.
Formulas for Power

P = Fv

Power = force x speed

P = Wk / t

Power = Work / Time
Units for Power

SI Unit = Watt (W)

Watt = 1 Joule/second

Horsepower (hp) is another unit of
power.

1 hp = 746 W
Practice Problem
How
long does it take a 19 kW
steam engine to do 6.8 x 10^7
J of work?