Forces and Vectors in Statics with Air Balloon Models

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Jot down everything you
know about VECTORS
 
 
m
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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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1
2
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h
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and magnitude 8 
N
W
B
3
Summary
You should be able to:
1 add and subtract forces, finding resultant force
2
 
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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
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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.

  • Forces
  • Vectors
  • Statics
  • Air Balloon
  • Trigonometry

Uploaded on Oct 04, 2024 | 0 Views


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Presentation Transcript


  1. Forces

  2. starter Jot down everything you know about VECTORS negative magnitude zero Add and subtract notation Parallel Perpendicular equal Multiply by a scalar

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. WB2 Work out the Forces i and j components for each step of the balloons journey: 450 22 300 36 600 33 25 750

  12. 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

  13. 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

  14. 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))

  15. 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

  16. 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

  17. END

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