06-4 Force Addition n Resolution

8/2/2019 06-4 Force Addition n Resolution

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Addition and resolution of forces


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1 Which of the following schoolbags

would you feel heavier to carry if thesame number of books are put in them?

A B


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2 A light rope is stretched tightly between

two poles.

What is the tension Tinthe string?

A T < 4 N

B T= 4 N

C T > 4 N

A T-shirt of weight 8 N is hung at themidpoint of the rope.

8 N


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Force is a vector quantity.

It has both magnitude and direction.

a Graphical method

Adding forces

Like displacements, forces can also be added graphicallyusing the 'tip-to-tail' method.

Lines representing forces should be drawn to scale.


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a Graphical method

Adding forces

F2

F1 F2+

F1

F2

F1

'Tip-to-tail' method

resultant

force


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a Graphical method

Adding forces

F2F1 F2+

F1

Parallelogram of forces method

resultantforce

parallel

parallel


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a Graphical method

Adding forces

Video

Simulation
http://../video/ch06/0612-add_forces.mpghttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../video/ch06/0612-add_forces.mpg


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Stretch a rubber band with a spring balance.

A

F

OB

F1

F2

Stretch the rubber band by the same amount using2 spring balances.

Addition of forces

Note the magnitude & direction of the F1 &F2.Check ifresultant = F(in magnitude & direction) by

using 'tip-to-tail' method

using parallelogram of forces method
http://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exehttp://../sim/sim0608.exe


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Addition of forces

Video
http://../sim/sim0608.exehttp://../video/ch06/0613-6g-add_forces.mpghttp://../video/ch06/0613-6g-add_forces.mpg


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b Algebraic method (1-dimension)1 Adding forces

F2F1

=F1 F2+F F2

F1

=F1 F2+F

Adding forces in the same

direction & along the same line.

The magnitude of the resultant force is thealgebraic sum of the forces.

direction is the sameas the forces

Adding forces in the opposite

direction & along the same line.

direction is the sameas the larger force


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c Algebraic method (2-demensions)

1 Adding forces

Forces in 2 dimensions can also be addedalgebraically. See this example:


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Use 1 cm to represent 25 000 NLength ofAC= 6.9 cm

Resultant

= 173 000 N

(with an of30 toeither force)

= 6.9 25 000 N

100 000 N 100 000 N

resultant

CExample 8

oil rig

A

B D

60


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= 5 N

tan =34

=36.9

22 43 R

R

= 36.9

3 N

4 N

5 N

Example 9

2 forces, 3 N and 4 N, act at right angles toeach other. Find the magnitude & directionof the resultant force.

Resultant force is 5 N with 36.9 tothe 4-N force.


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If Janice is pushing with a force of60 N &

Maximum force Minimum force

A 100 N 80 N

B 120 N 60 NC 140 N 20 N

D 160 N 40 N

Q1 If Janice is pushing with...

what are the maximum and the minimummagnitudes of their combined force?

Tommy is pushing with 80 N,


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Find the resultant of the forces

below with graphical method.

The resultant force is ________ N

making an angle __________ withthe 3-N force.

Q2 Find the resultant of the...

8.9

43

3 N

7 N

60(1 cm represents 1.5 N)


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2 ropes are used to pull a tree as shown.Q3 2 ropes are used to pull...

Find the magnitude of the resultant forceacting on the tree.

120 N

120 N

Magnitude ofresultant

= ____________

(Pythagoras theorem)

= ________ N

22 120120

170


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2 Resolving forces into

components

We 've learnt how to combine 2 forces into 1.

Let's see how to spilt (resolve) 1 force into 2.


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a Graphical method

Resolving forces into components

C

Fx

Fy

y

x

component

component

O

Suppose a force Fis represented by OC:

F

Magnitudes ofFx&Fycan be measureddirectly.


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b Algebraic method


Magnitudes ofFx&Fycan be also be found by

C

Fx

Fy

y

xO

F

F2= Fx2 + Fy

2

(Pythagoras theorem)

Fx= Fcos

Fy= Fsin

tan =F

x

Fy

algebraic method:


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b Algebraic method


Simulation
http://../sim/sim0609.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0609.exe


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2 tug boats pull an oil rig,each exerting a force of100 000 N, they are at

60

to each other.Find the resultant force.

Example 8
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A 1-kg trolley runs down a friction-compensated runway at a constant speed.

Hence find friction between trolley & runway.

Find the component of weight of the trolley

along runway,

= 20

Example 10

mass = 1 kg
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Weight (W) = mgComponent of weight along runway

= 10 N

= 10 sin 20= 3.42 N

W

20

= 20

mass = 1 kg

W

Component of weight along runway:

Example 10
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Friction between trolley & runway:

Example 10

constant speed

net force on trolley = 0

friction = 3.42 N (up the runway)

= 20

constant vfriction

component of weight

along runway = 3.42 N
http://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exe


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Example 11

12

Resolve tension along each rope into 2 components

along line of travel

normal to line of travel

180 cos 12 N

180 N 180 sin 12 N

Components in each direction are added
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180 N

200 N

12

10

A

B

C

15

Example 11

170 N

Total force along line of travel:180 cos 12 + 170 cos 10 + 200 cos (10+15)

= 525 N
http://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exe


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180 N

200 N

12

10

A

B

C

15

Example 11

170 N

Total force normal to line of travel:180 sin 12 170 cos 10 200 cos (10+15)

= 76.6 N

+ve
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tan =76.6

525

=8.30

N76.625252R +=

= 531 N

Resultant force exerted by the skiers is 531 Nat an angle of 8.30 to the line of travel.

Example 11

76.6 N

525 N

R
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Forces acting on 1-kg mass:

weight

But it is at rest, net force = 0

Implication:

equal & opposite to the3rd force

Resultant of any 2 forces

1-kg mass

in equilibrium

Forces in equilibrium

2 forces from 2 springs
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A 1-kg blockrests on a wedge.

Q1 A 1-kg block on rest on a...

What is the friction acting on the block?

Use graphical method to find the weightcomponents of the blockalong &normal tothe wedge.

A

B

C

O

30
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Weight componentalong

the wedge

= 10 _______

= ______ N

sin 30

cos 30

5

8.66

Q2 Find the weight components...

Find the weight componentsof the block by algebraicmethod.

A

B

C

O

at rest

30

Weight componentnormal to the wedge

= 10 _______

= _______ N
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A The 3-kg trolley moves downwards.

B Both trolleys remain at rest.

C The 2-kg trolley moves downwards.

Q3 What happens to the trolleys...

What happens to the trolleys when they

are released ? smooth pulley

20 30

3 kg 2 kg
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180 N

200 N

1210

A

B

C

15

Example 11

170 N

Find the magnitude & direction of theresultant force the skiers exert on thespeedboat?
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2 spring balances are used to support an 1-kgmass.

30

1-kg mass

F1F2

Example 12

What are the readings of the 2 balances?
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30 F2

F1

Example 12

F2F1

30

30

F110 N

= sin 3010F1F1 = 10sin 30 = 20 N

= tan 3010F2

F2 =10

tan 30= 17.3 N

The mass is in equilibrium.resultant force ofF2 & weight is equal & oppositeto F1
http://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exehttp://../sim/sim0901.exe


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F2

F1

30

The mass is in equilibrium.

horizontal resultant = 0

vertical resultant = 0

horizontal: F1 cos 30 = F2

vertical: F1 sin 30 = 10

F1= 20 N;

F2= 17.3 N

net force = 0 10 N

Example 12

Alternative method byresolution of forces
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06-4 Force Addition n Resolution

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