Grade 11 Mechanics Based on DocScientia Contains: Vectors in two dimensions Newton's Laws of motion Newton's Law of Universal Gravitation

1. Mechanics

2. Vectors in
two
dimensions

3. Physical quantity having
magnitude and a unit but
not direction.
DocScientia p. 12 Scalar definition

4. Physical quantity having
Magnitude, unit and
direction.
DocScientia p. 12 Vector definition

5. Graphical representation
of vectors
DocScientia p. 12

6. b
length
end (head)
a θ
start (tail)
DocScientia p. 12

7. Division of a vector into
components
DocScientia p. 12

8. one dimension vectors:
straight line ǁ to the
vertical or horisontal
axes
DocScientia p. 12

9. two dimension vectors:
form an angle to the
axes
DocScientia p. 12

10. components of a force
at an angle:
divided into 2 parts, 2 vectors
at ┴, same effect as
original vector
DocScientia p. 12

11. Fy F
Fx = Fcosθ
Fy = Fsinθ
r y
Cosθ = x/r = Fx/F
Sinθ = y/r = Fy/F
θ
x Fx
DocScientia p. 13

12. Object on slopes experience
forces like gravity that are
not ║ or ┴ to plane
DocScientia p. 14

13. Forces are divided with
respect to the plane.
DocScientia p. 13

14. Trig functions calculate the
components
DocScientia p. 13

15. cosθ = x/r = Fg┴/Fg
sinθ = y/r = Fg║/Fg
Fg┴ = Fgcosθ
Fg║
Fg║ = Fgsinθ
θ
r x
θ
Fg Fg┴
DocScientia p. 14 y

16. Pull or push
What is
a force Vector
F
N
→
Length = size
› = direction of force
DocScientia p. 20

17. forces
non-contact
A act over a distance
contact
B objects are in contact
with each other
DocScientia p. 20

18. non-contact forces
A act over a distance
Magnetic forces 1
Electrostatic forces 2
Gravitational forces 3
DocScientia p. 21

19. contact forces
B objects are in contact
with each other
Applied forces 1
Friction 2
Normal forces 3
DocScientia p. 21

20. contact forces
B objects are in contact
with each other
Tension 4
Air friction 5
Compression 6
DocScientia p. 21

21. contact forces
B objects are in contact
with each other
Applied forces 1
Same line as direction of motion
OR
At an agle to the direction of motion
DocScientia p. 21

22. contact forces
B objects are in contact
with each other
Friction 2
f or Ff tries to minimise motion, ∴
opposite direction to the movement
║ to contact surface
DocScientia p. 21

23. DocScientia p. 21

24. B 1
Same line as direction of motion
OR
At an agle to the direction of motion
Fg┴
Fy
Fx Fg║
DocScientia p. 21

25. contact forces
B objects are in contact
with each other
Normal forces (FN) 3
Force exerted by a surface on an object
on that surface
Always perpendicular to the surface
Supporting force is equal and opposite to
the force of the object
DocScientia p. 21

26. contact forces
B objects are in contact
with each other
Tension (FT) 4
Pulled cable/rope = tension
Tension is constant
Two directions
Mass = negligible, if asked to add:
Gravitational force will act on the
center of the rope
DocScientia p. 22

27. contact forces
B objects are in contact
with each other
Air friction (Fair) 5
Offer resistance to objects moving
through air
Acts in the opposite direction to
movement
DocScientia p. 22

28. contact forces
B objects are in contact
with each other
Compression (Fspring) 6
Equal in magnitude, exerted on any
object touching the spring
DocScientia p. 22

29. Forces and free body
diagrams
DocScientia p. 22

30. FN
F FN
F
o r f F
F
e
r f e
c Fg
e b
Fg o Object represented as
d a dot – can be a bit big
d Object w all forces y All forces = arrows w
i Simplify as block magnitude and
a Arrow shows d direction
g magnitude and i Arrows point away
direction a from the dot
r Arrow at position g Force @ angle is
a where force is r represented by either
m exerted a the force itself OR
DocScientia p. 22 m components

31. Friction force
DocScientia p. 28

32. Contact force
Two objects in close contact,
and it tries to move across
each other.
Surface of solids = generally
rough.
DocScientia p. 28

33. Uneven sections hook on
each other when sliding.
Friction = opposes motion
of two surfaces.
DocScientia p. 28

34. Factors that
influence the size
of the frictional
DocScientia p. 29
force
Surface type
Normal force

35. FN = Fg = w Fx = Fcosθ
Fx = Fcosθ F Fy = Fsinθ
Normal
N
Fy = Fsinθ FN = Fg – Fy
force
FN = Fg + Fy
Fg║
FN FN
Fg┴ Fy
Fg║=Fgsinθ
Fx Fg┴=Fgcosθ
Fy FN=Fgcosθ
Fx
θ
DocScientia p. 30
Fg

36. Surface
type Smooth tiles are very
slippery
Slightly melted ice on
an ice rink – it is easy
to glide
DocScientia p. 31

37. Surface
type The rougher the
surface,
the greater the
friction
DocScientia p. 31

38. The extent they affect
Surface
one another is
type
represented by the
coefficient
of friction
(μ)
DocScientia p. 31

39. Coefficient of friction
DocScientia p. 31

40. Symbol: μ
No unit – factor of roughness
Surface pairs have two
coefficients:
static friction: μs
kinetic friction: μk
DocScientia p. 31

41. Proportionality constant of
The relationship fαF is known
N
as the coefficient of friction
μs max > μk
The smaller the μ, the less
the resistance offered by a
surface, value < 1
DocScientia p. 31

42. How to reduce friction
DocScientia p. 31

43. Lubricate:
Oil
Grease
Finely powdered graphite
Wet the surface with water
DocScientia p. 31

44. Frictional force of one
contact surface
on another when there is no
relative motion
between the objects
DocScientia p. 32 Static friction (fs)

45. Independent of surface area
Dependent on mass & weight
→ mass + weight = FN
Depends on nature of surfaces
Acts opposite to motion
DocScientia p. 32

46. Directly proportional to the
normal force
DocScientia p. 32

47. Frictional force of one
contact surface
on another when one or both
objects are moving
DocScientia p. 32 Kinetic friction (fk)

48. Independent of surface area
Dependent on mass & weight
→ mass + weight = FN
Depends on nature of surfaces
Acts opposite to motion
DocScientia p. 32

49. Smaller than fs(max)
Directly proportional to the
normal force
DocScientia p. 32

50. Applied force, no motion:
fs = Fapplied Applied force increased, on the verge
of motion:
An object fs≤μsFN and fs(max)=μsFN fs(max) = FT
at rest on a but mass is the same No horisontal force:
fs(max) = μsFN
Fg, FN, fs are Fapplied = 0 N
rough unchanged Thus fs = 0 N
FN
horisontal
surface FT FT
f f
DocScientia p. 33
W

51. AppliedApplied force. @ angle:
When it force > fs(max)
Object begins to move. FN: FN = Fg – Fy
Get components
finally FrictionNonow kinetic. – fk = μFN
is vertical force
Applied push @ angle:
fk=µkGet∴fk = μ·(F – F ) = F + F
FN c mponents
starts to o g N
y g
No vertical motion: fk = μFN
y
move ∴fk = μ·(Fg + Fy)
on a
FN
FT F
FT
T
horisontal θθ
surface
f
W
DocScientia p. 34

52. @ rest: fs≤μsFN accelerating:
Graph of fs=μsFN
f
when an
Frictional force f (N)
About to start
moving
∴fs(max) = μsFs
Fk constant
object starts to
move over a
rough surface Applied force FT (N)
DocScientia p. 35

53. Object at rest: Fg║=Fgsinθ
Fg║and fs: equal and
An object Fg┴=Fgcosθ
opposite, fs=Fgsinθ
at rest on a
rough fs(max)=μsFN FN
surface fs(max)=μs(Fgcosθ)
@ an Fg║
fs
angl Fg┴
e θ w
DocScientia p. 35

54. Object at rest: Fg║=Fgsinθ
OBJECT SLIDING
Fg┴=Fgcosθ
Moving F fand F F ININ THE
and
f <f
DOWN A SLOPE
THE
kk s g║g║
on a SAMEk=ma
Fg║ - f DIRECTION
SAME DIRECTION
F-Fg║-fk=ma
F+Fg║-fF=ma F cosθ
fk=μk k N=μk g
FN
F
slope fk=μkFkN=μk(F(Fgcosθ)
fk=μ FN=μk cosθ)
g
@ an F Fg║
Fg┴
fk
fk
angl
e θ
DocScientia p. 35

55. Object at rest: Fg║=Fgsinθ
Fg┴=Fgcosθ
Moving
fs=Fg║=Fgsinθ
on a Object begins sliding
fs(max)=Fg║=Fgsinθ
slope fs(max)=μs·Fgcosθ
∴Fg·sinθ = μ·Fg·cosθ
@ an But fs(max)=μsFN
angl μs= Fgsinθ = tanθ
e
DocScientia p. 36 Fgsinθ

56. Applications of friction
Tyres vs road Walking/running over
surface loose sand/snow
Hand and lids of During road races
bottles velocity decreases
Soles of shoes Falling ouch!
and floor
Gears – motion
Stepping on
brakes
DocScientia p. 36

57. Forces in equilibrium
DocScientia p. 32

58. Σ forces on an object = 0.
Forces are balanced.
DocScientia p. 43 Equilibrium

59. Object is in equilibrium if:
Object is at Moves at a
constant
rest velocity
DocScientia p. 43

60. FN = Fg
FN
In opposite
Fg directions
DocScientia p. 43

61. @ constant height and velocity:
Lifting force
No acceleration – not vertically
nor horisontally
No net forces
Air resistance Applied force
Upwards lifting force =
gravitational force downwards
of the engine
Applied engine force = air
resistance weight
DocScientia p. 43

62. Forward force > resistance
Forward applied force
increases
Net force = forward
Plane will accelerate forward
DocScientia p. 44

63. Is the vector Σ of all the
forces acting on the object.
One force with the
same effect as all the
other forces together.
DocScientia p. 44 Resultant or net force Fnet

64. Determining the
resultant vector:
Trignometry to
Scale diagram;
2
3
1 Scale diagram;
calculate tail
head to the
tail to tail
components
(parallellogram)
DocScientia p. 44

65. Head to tail
Tail to tail
DocScientia p. 44

66. θ = 120°
100 N 140 N
DocScientia p. 44

67. Head to tail method Scale 1 cm:20 N
1 Axes
1 vector R = 6,3 cm
(from origin) = 126 N
2 New axes F = 100 N
= 5 cm
120 to the L 44°
2 vector 120°
3 Join tail of 1
to head of 2 F = 140 N = 7 cm
= resultant
DocScientia p. 45

68. Tail to tail method Scale 1 cm:20 N
1 Axes
1 vector from origin
Same axes
2 Measure 120
2 vector from origin
F = 100 N R = 6,3 cm
Parallellogram = 5 cm = 126 N
3 Diagonal from origin
No vector heads
touch 44°
Arrowhead
4 Measure length - N
Measure direction
120°
F = 140 N = 7 cm
DocScientia p. 46

69. Rough free body
1 diagram - no scale
Draw all x and y
components, use trig
2 to calculate each of
these components
Add all x componentsF = 100 N R = 126 N
3 and y components
Calculate
Use pythagoras to
calculate R.
Use tanƟ to
4 calculate angle
(with regards to x-
120°
F = 140 N
axis)
DocScientia p. 46

70. Newton's laws
of motion

72. 1
An object will stay at rest or continue to
move at a constant speed in a straight
line (at a constant velocity), unless
acted upon by an external net force.
Professor Mac Spock explains
DocScientia p 59 Newton's first law of motion/Law of inertia

73. The resistance of an object to a
change in its state of motion or
rest. Because of inertia objects
tend to remain at rest or continue at
uniform velocity.
DocScientia p 60 Inertia

74. Not a force – characteristic of
matter
Anything with mass has inertia
Mass is a measure of inertia
Greater mass = greater inertia
DocScientia p 60

75. In a frictionless system:
Ball reaches same
height as where the
motion starts, even
when the slope is
reduced.
Loss in height is due to
friction.
The ball would continue
to roll as long as there
DocScientia p 60
is no friction.

76. Net force is not necessary for continuous constant
motion in a straight line – it is needed to stop an
object.
DocScientia p 60

77. Protect against sudden
changes in motion.
According to Newton's
first law, a person will
continue to move until Seatbelt safety
something stops them.
DocScientia p 60

78. 2
If a net force acts on an object, the
object will accelerate in the direction of
the net force.
Acceleration is directly proportional to
net force and inversely proportional to
mass. Prof Mac
Second Law
Fnet = ma
DocScientia p 66 Newton's second law of motion

79. 3
If object A exerts a force on object B,
object B exerts an equal but opposite
force on object B.
1 2 3
DocScientia p 88 Newton's second law of motion

80. Newton's law of
universal gravitation

81. A force of gravitational attraction
exists between any two objects in the
universe that have mass.
This force of attraction is directly
proportional to the product of the
masses of the objects and inversely
proportional to the squared distance
between their centres of gravity.
DocScientia p 95 Law of universal gravitation

82. r
m1 F1 F2 m2
F = G m1m2
2
r
DocScientia p 96

83. Universal gravitational constant.
F = G m1m2
2
6,67x10
2
r -11
-2
N·m ·kg
On the information sheet
DocScientia p 97

84. Mass Weight
Definition Mass = Force with which the earth or
amount of another planet attracts an
matter. object.
Depends on the mass and
radius.
Scalar/ Scalar Vector
Vector
Formula Fg = mg
Unit kg Newton (N)
DocScientia p 97

85. weightlessness Weight is experienced indirectly due to
ical
gravity. echan
of m ity.
t re sult ra v
ad irec isti ng g
It is s re s Weightlessness
fo rce is when
gravitational force
is exerted on an object or
person.
The other mechanical
forces that cause the
feeling the feeling of
DocScientia p 98
weight are absent

86. Gravitational force surrounds everything that has mass.
Gg
Gravitational acceleration decreases
as the distance increases.
Gravitational acceleration (g) = 9,8 m·s-2
Weight = attractive force of the earth
on any object.
Gravitational force surrounds everything
that has mass. According to Newton: the
gravitational attraction between the earth
and the object.
DocScientia p 98

87. Gg
If one object is a planet
m and the other is an
object
the gravitational
attraction force is the
r weight.
The objects' mass is m,
M the planets' mass is M
and the distance (radius
of the planet) is r.
F = G mM mg = G mM g = G M
2 2 2
r r R
DocScientia p 98

88. All theory is taken from DocScientia text-
and workbook book 1, grade 11
Slide 1 – recruitingcycle.com
Slide 2 – womensquest.com
Slide 23 – cairoo software
Slide 32 – istockphoto.com
Slide 33 – visualphotos.com
Slide 66a – dreamstime.com
Slide 66b – langabi.name
Slide 70 – digimars.net
Slide 71 – TedEd on YouTube

89. Slide 75 – cairoo software
Slide 77 – fictionhealth.com
Slide 80 – fisica.cab.cnea.gov.ar