Mechaincom thechanies
Example A car acceleratesuniformlyfrom rest After 8s it has travelled mom
Calculate i its averageacceleration ii its instantaneousspeedafter8s
i S ut t tat
i 120 0 8 t tha 82 32A i a 3.75ms 2
ii V u't Zas
i Ot 26.75 120 900 v 30ms 1
FALLING OBJECTS
s n ar
us a
to
X
o ___
s i i
s
jatueforomi.gl
I 2 t i z 3 t
Yon i
20 1
i
i
with air
resistance
l
o i
i
i
I 2 3T
PROJECTILE MOTION
Horizontal Vertical Components
IEoesntianThe'Erraigonntalairection
i yYh T
un
Example
h
q
V Th g
µ
, A
verticalmotion
s ut t t at so h O t t lo t2
2
701 it s
since v u tat v O t lo
iron m5
Horizontalmotion
UH x t Un Eh
i the final velocity is the vectoradditionof v and Ua
FORCES ASVECTORS
a
by vector mathematics resultant
P surfaceforce forge µ
Illf
weight
X p
b
by components i resultant down slope
r
compenenwetointooscope
Wsino
resultantintoslope
WoosO R
JO µ componentdownslope
O
Wsino
NEWTONS LAWS
An objectcontinues in uniform motion in a straight line or at rest unless
a resultantexternal force acts
Equilibrium Translational Equilibrium
EF zero
An object that is constantly at rest
An object that is moving withconstant uniform velocity in a straight line
, g y g
tension G If inequilibrium
µ Tsin O P no resultant Fenorizontal
Iii
Toso W noresultant Frertica
iii freight
The resultant force is proportional to the rate ofchange of momentum
F
SI
at
The resultantforce is proportional to the acceleration
F ma
7 5ms Z F ma
ZN F 3 1.5 4.5 N
3kg frictionforce
ForwardForce Friction Fresutant
friction Fforward fresultant
12 4.5 7,5 N
r
3mg I intoscopei Fn componentintoslope
imp
Block doesn't accelerate into
Slope
mpmdam
theslope
downtheslope
Componentdownslope _30N sin30
G 15N
F Ma Max Ff up 8N
i acceleration down slope Fresuitant down 15 8 7N
Th
tm ZI 2.3ms
When two bodies A 4 B interact the force that A exerts on B
is equal and opposite to the force that B exerts on A
Equal bot opposite force
FAB Fisa
, Pushotthewall Pushofthe
on the girl the wall
girl
Jon
EE
hit
COEFFICIENT OF FRICTION
Fmax 1413
where R normalreactionforce
freaction spuy
friction V Md Ms
W
Example r
If balanced F Wsind
T 1 componentotwinto
slope
R NcosO
componentof Woof 0 is increased whenblockjuststarts
wdownslope moving F Fmax
Wsing TO
µ Fyfe Wwsion ta
Work if
Workdone Fscoso
1
i t
The total work done is the area under
Examples theforce displacementgraph
For spring'd
F kx
sting Through.pe
in
t I
xmaextension
, ENERGY ANDPOWER
The amount ofenergytransferred is equalto the workdone
Overall the total energyof anyclosedsystemmustbe constant
Energy is neithercreated nordestroyed it just changesform
There is no change in the total energy in the Universe
MUZ I
KE 2M
GravitationalPotentialenergy mgh
Elastic PotentialEnergy Tk si K springconstant
Power
energytransferrede
workdonetime
taken timetaken
Efficiency useful
energylwo.ru
power0UTtotalpower
energypower IN
Example A grasshopper m uses its hind
8g legs to push for 0 Is and as
a result jumps 1.8 m high Calculate its take off speed Pdeveloped
i PE gained Mgh
Izmir mgh conservation ofenergy
mu
KE at start
v Mgh M 58 Gms
ii Power Mfd 0.0081.82
10 x 1.4 W
O l
A 60W lightbulb has an efficiency of 10 How muchenergy is
wasted everyhour
Power wasted 90 of 60W 54W
Energywasted 54 60 60J 190k
Momentum d impulse
p MV
Example A car acceleratesuniformlyfrom rest After 8s it has travelled mom
Calculate i its averageacceleration ii its instantaneousspeedafter8s
i S ut t tat
i 120 0 8 t tha 82 32A i a 3.75ms 2
ii V u't Zas
i Ot 26.75 120 900 v 30ms 1
FALLING OBJECTS
s n ar
us a
to
X
o ___
s i i
s
jatueforomi.gl
I 2 t i z 3 t
Yon i
20 1
i
i
with air
resistance
l
o i
i
i
I 2 3T
PROJECTILE MOTION
Horizontal Vertical Components
IEoesntianThe'Erraigonntalairection
i yYh T
un
Example
h
q
V Th g
µ
, A
verticalmotion
s ut t t at so h O t t lo t2
2
701 it s
since v u tat v O t lo
iron m5
Horizontalmotion
UH x t Un Eh
i the final velocity is the vectoradditionof v and Ua
FORCES ASVECTORS
a
by vector mathematics resultant
P surfaceforce forge µ
Illf
weight
X p
b
by components i resultant down slope
r
compenenwetointooscope
Wsino
resultantintoslope
WoosO R
JO µ componentdownslope
O
Wsino
NEWTONS LAWS
An objectcontinues in uniform motion in a straight line or at rest unless
a resultantexternal force acts
Equilibrium Translational Equilibrium
EF zero
An object that is constantly at rest
An object that is moving withconstant uniform velocity in a straight line
, g y g
tension G If inequilibrium
µ Tsin O P no resultant Fenorizontal
Iii
Toso W noresultant Frertica
iii freight
The resultant force is proportional to the rate ofchange of momentum
F
SI
at
The resultantforce is proportional to the acceleration
F ma
7 5ms Z F ma
ZN F 3 1.5 4.5 N
3kg frictionforce
ForwardForce Friction Fresutant
friction Fforward fresultant
12 4.5 7,5 N
r
3mg I intoscopei Fn componentintoslope
imp
Block doesn't accelerate into
Slope
mpmdam
theslope
downtheslope
Componentdownslope _30N sin30
G 15N
F Ma Max Ff up 8N
i acceleration down slope Fresuitant down 15 8 7N
Th
tm ZI 2.3ms
When two bodies A 4 B interact the force that A exerts on B
is equal and opposite to the force that B exerts on A
Equal bot opposite force
FAB Fisa
, Pushotthewall Pushofthe
on the girl the wall
girl
Jon
EE
hit
COEFFICIENT OF FRICTION
Fmax 1413
where R normalreactionforce
freaction spuy
friction V Md Ms
W
Example r
If balanced F Wsind
T 1 componentotwinto
slope
R NcosO
componentof Woof 0 is increased whenblockjuststarts
wdownslope moving F Fmax
Wsing TO
µ Fyfe Wwsion ta
Work if
Workdone Fscoso
1
i t
The total work done is the area under
Examples theforce displacementgraph
For spring'd
F kx
sting Through.pe
in
t I
xmaextension
, ENERGY ANDPOWER
The amount ofenergytransferred is equalto the workdone
Overall the total energyof anyclosedsystemmustbe constant
Energy is neithercreated nordestroyed it just changesform
There is no change in the total energy in the Universe
MUZ I
KE 2M
GravitationalPotentialenergy mgh
Elastic PotentialEnergy Tk si K springconstant
Power
energytransferrede
workdonetime
taken timetaken
Efficiency useful
energylwo.ru
power0UTtotalpower
energypower IN
Example A grasshopper m uses its hind
8g legs to push for 0 Is and as
a result jumps 1.8 m high Calculate its take off speed Pdeveloped
i PE gained Mgh
Izmir mgh conservation ofenergy
mu
KE at start
v Mgh M 58 Gms
ii Power Mfd 0.0081.82
10 x 1.4 W
O l
A 60W lightbulb has an efficiency of 10 How muchenergy is
wasted everyhour
Power wasted 90 of 60W 54W
Energywasted 54 60 60J 190k
Momentum d impulse
p MV
