Notesale: Turn your study into money

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Vectors and Scalars
Scalars- fully described by their magnitude
Vectors- fully described by their magnitude and direction
Scalars
Speed
Distance
Time
Energy
Temperature
Pressure
Mass
power

Vectors
Displacement
Velocity
Weight
Force
Momentum
Acceleration
impulse

Vector Diagrams
The resultant of two or more vectors which act at an angle to each other can be found by
drawing a vector diagram
...

u= initial velocity (ms-1), v= final velocity (ms-1), s= displacement (m) , a= acceleration
(ms-2), t= time(s)
1)
2)
3)
4)
5)

v=u+at
s= ut + ½ at2
v2 = u2 + 2as
s= ½(u+v)t
s= vt- ½ at2

Newton’s Laws of Motion
1) An object will remain at rest or travel at a constant velocity unless acted upon by an
unbalanced force
2) If an unbalanced force acts on an object then the object will accelerate in the
direction of the unbalanced force
F= m a
F= force (N)
m= mass (kg)
a=
acceleration (ms-2 )
3) For every action there is an equal and opposite reaction

Motion Down a Slope
component of weight parallel to the
slope = mg sin Θ
Component of weight perpendicular
to the slope = mg cos Θ
Weight = mg
Frictional Force
Reaction Force





If the object has a constant velocity then the frictional forces must be equal to the
component of the weight down a slope
As the angle of the slope increases, the acceleration down the slope increases
The acceleration down the slope is not proportional to the angle of the slope
Components of a Force

Any force can be split into its horizontal and vertical components
...
i
...
weight
is equal to air resistance
Aunbalanced force acts downwards and accelerates
BAir resistance = weight- constant velocity – terminal
velocity
CAir resistance increases- unbalanced force upwardsdecelerates
D-

Forced balanced- constant velocity

Lifts
If you weigh yourself whilst in a lift, the reading on the scale will be an indication of the
unbalanced force acting on you
...

Stationary

W=T

Accelerating downwards

W more than T

Constant velocity

W=T

Decelerating downwards

T more than W

Stationary

W=T

Rockets




The acceleration of a rocket will increase
This is because the rocket burns fuel and this reduces the overall mass and weight of
the rocket- F=ma
The air resistance also decreases as the rocket gets further away from the Earth

Tension
Object A is pulling object B
...
The total force exerted through the string
is called the tension
...
5

15= 10 x a

= 3N

a = 1
...


p = mv
p = momentum (kgms-1 )


m= mass (kg)

v= velocity (ms -1)

the initial or final velocity of one of the objects in a collision can be calculated
by calculating the total momentum either before or after the collision, and
using the principle of conservation of momentum

Energy and Power


work is done when a force is applied to move an object through any distance
Ew = F d

Ew = Work Done (J)


F= Force (N)

d = distance (m)

The kinetic energy of an object is the energy that the object possesses due to
its motion
...

Ek = ½ m v2

Ek = kinetic energy (J)


m= mass (kg)

v = velocity (ms -1)

Gravitational potential energy is the energy that an object gains when it is
raised above the surface of the earth
...
g
...
67 x10-11 m3 kg-1 s-2
r = distance between the two objects



Special Relativity
Newtonian relativity said that space and time were absolute
...

It is only significant when one of the observers is moving relative to the speed of
light
...

It is only significant when the object is travelling at a velocity close to the speed of
light

l’ = length measured in a frame of reference moving relative to that of the object
l = length of the object in its own frame of reference
v= relative velocity of the two frames of reference
c= speed of light

Doppler Effect
The Doppler effect is the apparent change in frequency which occurs when a source of
waves and an observer are moving relative to each other
...




Recessional velocity formula is only used for galaxies moving at less then 10% of the
speed of light

Hubble’s Law


Galaxies are moving away from us and their recessional velocity increases the
further away they are









The recessional velocity
varies directly with the
distance
This is known as Hubble’s
law
The gradient of the graph is
equal to Hubble’s constant

V= Hod
V= recessional velocity
Ho = Hubble’s constant (s-1 ) d= distance from us (m)
Dark energy- the mass of the universe is estimated to be more than the mass of the
observable universe so matter must exist which does not give off any
electromagnetic radiation
Dark energy- the expansion rate of the universe is increasing with time- this must be
due to dark energy which cannot be detected, fighting against the gravitational
attraction between all the objects in the universe



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