Forces and Vectors in Statics with Air Balloon Models
starter
Jot down everything you
know about VECTORS
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Force Diagrams Hot air balloon
Use trigonometry to find the components of a vector
(or magnitude and direction)
Find the resultant of two or more forces
,
as the sum
of components
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Force diagrams intro 1
An air balloon is modelled as acting according
to the following forces:
i)
Lift
ii)
Wind
iii)
Weight
iv)
Air resistance
Model assumptions
Model assumptions
An air balloon is modelled as acting according
to the following forces:
i)
Lift
ii)
Wind
iii)
Weight
iv)
Air resistance
i)
The balloon is modelled as a particle (point)
ii)
The forces are constant
iii)
No other forces are involved
Force diagrams Intro 2
What will the air balloon do if these forces are
i)
Lift 200 N
ii)
Wind east 120 N
iii)
Weight 180 N
iv)
Air 70 N
resistance
Lift
-
Weight =
20 N upwards
Wind
-
resistance
=
50 N East
50
i
+ 20
j
i
is 1 unit along
j
is 1 unit up
RESULTANT force
“The balloon is modelled as a particle”
Force diagrams Intro 3
The balloonists throw out sandbags
and the wind dies down
i)
Lift 200 N
ii)
Wind east 50 N
iii)
Weight 165 N
iv)
Air 70 N
resistance
Lift
-
Weight =
35 N upwards
Wind
-
resistance
=
-20 N East
-20
i
+ 35
j
RESULTANT force
Force diagrams Intro 4
The balloonist reduces the flame and the wind changes direction
i)
Lift 110 N
ii)
Wind west 100 N
iii)
Weight 165 N
iv)
Air 70 N
resistance
Lift
-
Weight =
-55 N
downwards
Wind
-
resistance
=
-30 N
East
-30
i
- 55
j
RESULTANT force
Force diagrams Intro 5 Split into components
The balloon is being pushed by resultant force 120 N in a
North east direction
Lift
-
Weight =
?
Wind
-
resistance
=
?
?
i
+ ?
j
120
45
0
120 sin45
= 84.9
120 cos45
= 84.9
84.9
i
+ 84.9
j
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:
7
11
16
8
140
0
60
0
50
0
20
0
7 sin 60
7 cos 60
-11 sin 50
-8 sin 20
16 sin 40
11 cos 50
-8 cos 20
-16 cos 40
40
0
W
B
1
Work out the Forces
i
and
j
components for each step of the balloons journey:
22
33
36
75
0
30
0
45
0
60
0
25
W
B
2
Force diagrams Intro 7 magnitude and direction
What if we want the direction and magnitude of the resultant force
Magnitude =
i)
Lift 200 N
ii)
Wind east 120 N
iii)
Weight 180 N
iv)
Air 70 N
resistance
Lift
-
Weight =
20 N upwards
Wind
-
resistance
=
50 N East
50
i
+ 20
j
50
20
Direction =
upwards from the horizontal
Work out the direction and magnitude of each force:
5
i
+ 3
j
-4
i
- 7
j
12i
- 8
j
Direction 31
0
up from horizontal
and magnitude 5.83
N
Direction 34
0
down from horizontal
and magnitude 14.4
N
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and magnitude 8
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Summary
You should be able to:
1 add and subtract forces, finding resultant force
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a
To find the magnitude of a Force use
Pythagoras
To find the direction of a Force use
Trigonometry
(arctan (tan
-1
))
A
F
F sin A
F cos A
Plenary
Discuss: In what context will we find
Forces? What type of problems?
engineering and building: strengths of materials
holding up walls, floors, bridges …
sailing: forces = currents in the water and drive
of the engine
connected objects: car pulling a caravan; objects
suspended by cables from cranes …
self-assess
One thing learned is –
One thing to improve is –
Force Diagrams Hot air balloon
Use trigonometry to find the components of a vector
(or magnitude and direction)
Find the resultant of two or more forces
, as the sum
of components
END
Explore the world of forces and vectors in statics through the model of a hot air balloon. Learn about vectors of negative magnitude, zero, addition, subtraction, parallel and perpendicular components, and multiplying by a scalar. Discover how to find components and the resultant force of multiple forces using trigonometry. Dive into real-life situations where terms like air resistance, weight, and force resolution are applied.
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Presentation Transcript
starter Jot down everything you know about VECTORS negative magnitude zero Add and subtract notation Parallel Perpendicular equal Multiply by a scalar
Statics Force diagrams Force Diagrams Hot air balloon Use trigonometry to find the components of a vector (or magnitude and direction) Find the resultant of two or more forces, as the sum of components Starter: think of a situation in real life that these terms would be used Air Resistance Weight Force resolving magnitude direction
Force diagrams intro 1 An air balloon is modelled as acting according to the following forces: i) Lift ii) Wind iii) Weight iv) Air resistance Model assumptions Model assumptions
Model assumptions An air balloon is modelled as acting according to the following forces: i) Lift ii) Wind iii) Weight iv) Air resistance i) The balloon is modelled as a particle (point) ii) The forces are constant iii) No other forces are involved
Force diagrams Intro 2 What will the air balloon do if these forces are i) Lift 200 N ii) Wind east 120 N iii) Weight 180 N iv) Air 70 N resistance RESULTANT force 50i + 20j Lift - Weight = 20 N upwards i is 1 unit along Wind - resistance = 50 N East j is 1 unit up The balloon is modelled as a particle
Force diagrams Intro 3 The balloonists throw out sandbags and the wind dies down RESULTANT force -20i + 35j i) Lift 200 N ii) Wind east 50 N iii) Weight 165 N iv) Air 70 N resistance Lift - Weight = 35 N upwards Wind - resistance = -20 N East
Force diagrams Intro 4 The balloonist reduces the flame and the wind changes direction i) Lift 110 N ii) Wind west 100 N iii) Weight 165 N iv) Air 70 N resistance Lift - Weight = -55 N downwards Wind - resistance = -30 N East -30i - 55j RESULTANT force
Force diagrams Intro 5 Split into components The balloon is being pushed by resultant force 120 N in a North east direction ?i + ?j Lift - Weight = ? Wind - resistance = ? 84.9i + 84.9j 120 450 120 sin45 = 84.9 120 cos45 = 84.9
WB1 Work out the Forces i i andj jcomponents: 11 cos 50 7 500 7 sin 60 -11 sin 50 11 600 7 cos 60 -8 cos 20 200 16 16 sin 40 -8 sin 20 8 1400 400 -16 cos 40
WB2 Work out the Forces i and j components for each step of the balloons journey: 450 22 300 36 600 33 25 750
Force diagrams Intro 7 magnitude and direction What if we want the direction and magnitude of the resultant force i) ii) iii) Weight 180 N iv) Air 70 N resistance Lift 200 N Wind east 120 N 50i + 20j Lift - Weight = 20 N upwards Wind - resistance = 50 N East Magnitude = + = 2 2 50 20 53 9 . N 20 Direction = upwards from the horizontal 0 = 1 tan 21 8 . 20 50 50
WB3 Work out the direction and magnitude of each force: 0 = 1 tan 33 7 . 8 12 5i + 3j + = 2 2 12 8 14 42 . Direction 340 down from horizontal and magnitude 14.4 N 0 = 1 tan 31 3 5 + = 2 2 5 3 . 5 83 12i - 8j Direction 310 up from horizontal and magnitude 5.83 N 0 = 1 tan 60 3 . 7 4 + = 2 2 4 7 . 8 06 -4i - 7j Direction 1200down from horizontal and magnitude 8 N
Summary You should be able to: 1 add and subtract forces, finding resultant force 2 resolve forces into i and j components 3 resolve i and j components into magnitude and direction or vice versa F F sin A A F cos A To find the magnitude of a Force use Pythagoras To find the direction of a Force use Trigonometry (arctan (tan-1))
Plenary Discuss: In what context will we find Forces? What type of problems? engineering and building: strengths of materials holding up walls, floors, bridges sailing: forces = currents in the water and drive of the engine connected objects: car pulling a caravan; objects suspended by cables from cranes
Force Diagrams Hot air balloon Use trigonometry to find the components of a vector (or magnitude and direction) Find the resultant of two or more forces, as the sum of components self-assess One thing learned is One thing to improve is
