Physics

1. Section 5-1

2. 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.

3.  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.

4. 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).

5. 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.

6. 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.

7. 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.

8. 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.

9. Guided Practice
 Pg. 169 Sample 5A

10. Section 2 Energy
Kinetic Energy
Work-Kinetic Energy Theorem

11. 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

12. 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.

13. 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.

14. Let’s Practice some problems…
 Open your books to pg. 173 and work
sample problem 5B

15. 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
Wnet = Δ KE
Wnet = KEf - KEi
Fnet d(cos θ) = ½ mv2
f – ½
mv2
i

16. 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

17. Section 3
Conservation of
Mechanical Energy

18. 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.

19. Conserved Quantity
 The mass of the light bulb whether whole or
in pieces is constant and thus conserved.

20. 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.

21. 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

23. Mechanical Energy
 Formula :
 MEi = MEf
 MEi = PEi + Kei
 MEf = PEf + Kef
 Therefore :
 PEi + KEi = PEf + KEf

24. Practice Problem
 Pg. 184 Sample Problem 5E

25. Section 4
Power

26. 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.

27. Formulas for Power
 P = Fv
 Power = force x speed
 P = Wk / t
 Power = Work / Time

28. Units for Power
 SI Unit = Watt (W)
 Watt = 1 Joule/second
 Horsepower (hp) is another unit of
power.
 1 hp = 746 W

29. Practice Problem
How long does it take a 19 kW
steam engine to do 6.8 x 10^7
J of work?