REVISIONNEWTON’S LAW

Quantity with magnitude and direction.

e.g. displacement, velocity, acceleration, force and weight..

VECTORQuantity having only

magnitude, not direction. e.g. distance, speed, mass

SCALAR

Earth's gravitational pull on an object.

It is measured in Newton

WEIGHTThe measure of the amount of matter

contained in the object.It is measured in kilograms

MASS

RESULTANTE/NET VECTOR The single vector that will have the same effect as all the other

vectors will have together

FORCES

WEI

GHT

NO

RMAL FO

RCE

APPLIED FORCE

DIRECTION OF MOTION

FRICTIONAL FORCE

FORCE DIAGRAM

FREE BODYDIAGRAM

normaal forceF Gravitational force (weight)

kinetic frictional forceF force of cat on box

N

g

k

T

KEYF

f

DIRECTIONS

• 300o • 30o North of West • West 30o North

NEWTON'S FIRST LAW OF MOTIONA body will remain in its state of rest or motion at

constant velocity unless a non-zero resultant/net force acts on it.

NEWTON'S SECOND LAW OF MOTION

When a resultant/net force acts on an object, the object will accelerate in the direction of the force at an acceleration directly

proportional to the force and inversely proportional to the mass of the object.

Fres=ma

NEWTON'S THIRD LAW OF MOTIONWhen one body exerts a force on a second body, the second body exerts a force of equal magnitude in the

opposite direction on the first body

NEWTON'S THIRD LAWACTION-REACTION PAIRS1. Same magnitude, opposite direction2. Simultaneous3. Only two objects

the force or the component of a force which a surface exerts on an object with which it is in contact, and which is perpendicular to

the surface

NORMAL FORCE

WEIGHTgravitational force the Earth exerts on any object on or near its

surface

the force that opposes the motion of an object acts parallel to the surface.

– Perpendicular on normal force– independent of the area of

contact – independent of the velocity of

motion

FRICTIONAL FORCE

STATIC FRICTIONAL FORCE the force that opposes the tendency

of motion of a stationary object relative to a surface

KINETIC FRICTIONAL FORCE the force that opposes the motion of a

moving object relative to a surface

Nf F

• Is usually given• It depends on the 2 surface areas that are in

DIRECT contact• This is the relationship between the friction force

and the normal force of an object (the coefficient of friction therefor has no unit of measure)

COEFFICIENT OF FRICTION

N

fF

Forces acting on an object. Pushing or pulling forces

APPLIED FORCE

TENSION Force in a stretched rope

RESULTANT / NET VECTORThe single force that will have the same effect as all the other

forces will have together

FORCE DIAGRAMS

FORCE DIAGRAMS

FORCE DIAGRAMS

normal forceF Gravitation (weight)

frictionF Applied force

N

g

T

F

f

sin cos

cossin

cossin

y x

TT

x Ty T

o ah hF F

FFF FF F

normal forceF Gravitation (weight)

frictionF Vertical komponent of pplied force

F Horizontal komonent of pplied force

N

g

y

x

F

fa

a

FORCE DIAGRAMS

FORCE DIAGRAMS

||

normal forcefriction

F Vertical komponent of weight

F Vertical komponent of weight

N

g

g

Ff

||

||

sin cos

sin cos

sin cos

g g

g g

g g g g

o ah hF F

F F

F F F F

EQUILIBRIUMNEWTON’S PROBLEMS

PERPENDICULAR FORCES (equilibrium)

‘ANGLED’ FORCES (equilibrium)

A box with mass 5kg stands stationary on a horizontal plane, experiencing a 10N applied force at an angle of 30o

ANGLED PLANES (equilibrium)

TRIANGLES for EQUILIBRIUM with THREE FORCES

non-EQUILIBRIUMNEWTON’S PROBLEMS

PERPENDICULAR FORCES (non-equilibrium)

‘ANGLED’ FORCES (non-equilibrium)

o

A block of mass 1 kg is connected to another block of mass 4 kg by a light inextensible string.

The system is pulled up a rough plane inclined at 30 to the horizontal, by means of a constant 40 N force parallel to the plane as shown in the diagram above.The magnitude of the kinetic frictional force between the surface and the 4 kg block is 10 N. The coefficient of kinetic friction between the 1 k

g block and the surface is 0,29. State Newton's third law in words.

Draw a labelled free-body diagram showing ALL the forces acting on the 1 kg block as it moves up the incline.

Calculate the magnit

a

b

ude of the: Kinetic frictional force between the 1 kg block and the surface

Tension in the string connecting the two blocks

c

d

||

||

o o

For the 1kg block

sin cos

sin cos

sin cos

1 9.8 sin 30 1 9.8 cos 30

g g

g g

g g g g

o ah hF F

F F

F F F F

||

||

o o

For the 4kg block

sin cos

sin cos

sin cos

4 9.8 sin 30 4 9.8 cos 30

g g

g g

g g g g

o ah hF F

F F

F F F F

o

see left

0.29 8.48take up as positive2.46 down

0

1 9.8 cos 308.48

N

res

N g

N g

ay axis f Fb

F ma NF F

F F

N

||

o

for 1kg block-

take up as positiveF

40 2.45 1 9.8 sin 30 132.6 1

for 4kg block

res

T g

cx axis

maF f T F ma

T aT a

||

o

for 4kg block-

take 'up' as positiveF

10 4 9.8 sin 30 429.6 4

res

g

c

x axis

maT f F ma

T aT a

2

T=T Susbtitute a in 29.6 432.6 1 29.6 4 29.6 4 0.6

3.03 5 32.030.6 . up

let T aa a

a Na m s

||

||

o o

For the 1kg block

sin cos

sin cos

sin cos

1 9.8 sin 30 1 9.8 cos 30

g g

g g

g g g g

o ah hF F

F F

F F F F

||

||

o o

For the 4kg block

sin cos

sin cos

sin cos

4 9.8 sin 30 4 9.8 cos 30

g g

g g

g g g g

o ah hF F

F F

F F F F

o

||

o

see left

0.29 8.48take up as positive2.46 up

0

1 9.8 cos 30

8.48for 1kg block

-take up as positive

F

40 2.45 1 9.8 sin 30 1

32.6 1for 4kg bloc

N

res

N g

N g

res

T g

a

y axis f Fb

F ma NF F

F F

Nc

x axis

maF f T F ma

T a

T a

||

o

2

k-

take 'up' as positiveF

10 4 9.8 sin 30 4

29.6 4

T=T Susbtitute a in 29.6 432.6 1 29.6 4 29.6 4 0.6

3.03 5 32.030.6 . up

res

g

x axis

maT f F ma

T a

T a

let T aa a

a Na m s

ELEVATORS

GRAPHIC SOLUTIONSNEWTON’S PROBLEMS

HEAD-TO-TAIL METHOD– EQUILIBRIUM with THREE FORCES

HEAD-TO-TAIL METHOD– EQUILIBRIUM with maximum

tension/weight

GRAPHIC SOLUTIONS for NON-EQUILIBRIUM

NEWTON’S UNIVERSAL GRAVITATIONAL LAW

NEWTON'S UNIVERSAL GRAVITATION LAW

Each body in the universe attracts every other body with a force that is directly proportional to the

product of their masses and inversely proportional to the square of the distance between their centres

1 22

Gm mF

r

GRAVITATIONAL ACCELERATION FOR ANY PLANET1 22 g

Gm mF F mg

r

2

2

2

g

o po

o p

o

p

F F

Gm mm g

rGm m

gr mGm

gr

There is a gravitational force F between objects A and B at a distance R from each other. What will the gravitational force be if the mass of A is doubled and the distance of separation

made three ti 29mes greater ? F

RATIO PROBLEMS

RATIO PROBLEMS

22 2

2 2

2

3

2329

A B Ai f

A B

i

km m k m mF FR R

km mR

F

363  , 517    aThree spheres li

nd 154 e stationary in a straight line.

The masses of the spheres are Determine the magnitude and direction of the net gravitatio ...

Sphere A

nal force

5.7

onA B Cm kg m kg m kg

a

5

5

5

10 right

3.5 10 right  Sphere B

Sph 9 10 er lefe C t

b

c

N

N

N

NET GRAVITATIONAL FORCE

NET GRAVITATIONAL FORCE

2

11

2

11 5

2

11

2

11 6

between A & B?363517 6.67 10 363 5170.5 0.5

6.67 10 5 10 between A & C

?363154 6.67 10 363 1540.75 0.7

take right

56.67 10 6.6 10

AB A BAB

ABA

B

AB

AB A CAC

ACA

C

AC

FF Gm m

Frm

mr

G NF

F Gm mF

rmmr

G N

5 6

5

:

5 10 6.6 10

5.7 10 re

as posit

gs

ive

net AB ACA F F Fa

N

NET GRAVITATIONAL FORCE

2

11

2

11 5

2

11

2

11 5

between A & B?363517 6.67 10 363 5170.5 0.5

6.67 10 5 10 between B & C

?517154 6.67 10 517 1540.25 0.2

take right

56.67 10 8.5 10

AB A BAB

ABA

B

AB

AB B CBC

BCB

C

BC

FF Gm m

Frm

mr

G NF

F Gm mF

rmmr

G N

5 5

5

:

8.5 10

as posit

5 10

3.5 10 re

v

gs

i e

net BC ABB F F Fb

N

NET GRAVITATIONAL FORCE

2

11

2

11 6

2

11

2

11 5

between A & C?363154 6.67 10 363 1540.75 0.75

6.67 10 6.6 10 between B & C

?517154 6.67 10 517 1540.25 0.25

6.67 10 8.5r

10take

AB A CAC

ACA

C

AC

AB B CBC

BCB

C

BC

FF Gm m

Frm

mr

G NF

F Gm mF

rmmr

G N

6 5

5

5

:

6.6 10 8.5 10

9 10

9 10 l

ight as positive

inks

net AC BCC F F Fc

N

N