Our Dynamic Universe Flashcards
scalar
a quantity that consists of a magnitude only
e.g. energy, mass, temperature, power
vector
a quantity that consists of a magnitude and direction
e.g. force, acceleration, momentum, displacement
distance
d
how for an object has travelled from the starting point to the finishing point of a journey, regardless of direction
scalar
displacement
s
- the shortest distance between the starting point and the finishing point of a journey, which takes into the acount the direction of travel
- given by the area under a velocity time graph
vector quantity
speed
v
the distance travelled per unit time
scalar
velocity
v
the displacement per unit time
vector
average speed
the total distance travelled by an object over the total time taken
average velocity
the total displacement of an object over the total time taken
velocity-time graphs
sign convention
- upwards and right = +ve
- down and left = -ve
- a horizontal line on a v-t graph represents constant velocity
- positive m = uniform acceleration; negative m = uniform decceleration
equations of motion
suvat
- v = u + at
- s = ut + 1/2at2
- v2 = u2 + 2as
- s = 1/2(v + u)t
acceleration
a
- the change in velocity per unit time
- rate of change of velocity
- given by the gradient on a v-t graph
vector
decceleration
a
a negative acceleration showing that an object is slowing down
friction
a force, between two objects, which opposes the motion of an object
drag
a force, between a solid and a liquid (often water), which opposes the motion of an object
air resistance
a force, between a solid object and air paticles (gas), which opposes the motion of an object
balanced forces
- when the vector sum of all the forces is equal to zero
- the forces are often equal in magnitude, and opposite in direction
=0
unbalanced forces
when the vector sum of all the forces is not equal to zero
≠0
newtons laws of motion
1
an object will remain at rest or at a constant velocity unless acted upon by an external unbalanced force
newtons laws of motion
2
- the acceleration of an object is proportional to the unbalanced force acting on it and inversly propotional to the mass of the object
- Funbalanced = ma
newtons laws of motion
3
- if object A exerts a force on object B, then B will exert an equal and opposite force on A
- for every action there is an equal and opposite reaction
newtons pairs
- action and rection forces for situations involving newtons 3rd law
- example: person on skateboard exerts a force on the wall, the wall exerts a force on the person therefore the skateboard moves
rockets
newtons laws of motion
- newtons 3rd law explains the launch - rocket motors push hot gases downwards (action), hot gases push back on rocket (reaction)
- the force acting on the rocket is unbalanced therefore newtons 2nd law explains its acceleration
- air resistance, mass of fuel, and gravitational field strength also affect the magnitude of the unbalanced force
tension
the pulling force on a bar, string, rope, cable, or chain
free-fall
describes the movement of an object under the influence of gravity alone
terminal velocity
for an object in free-fall, a constant speed is reached when the upward force acting on the object (air resistance) is balaced by the downward force acting on the object (weight)
acceleration due to gravity
9.8 ms-2
in the absense of air resistance (on earth)
gravitational field strength
g
- the weight acting per unit mass on an object
- measured in Nkg-1
9.8 Nkg-1 on earth
mass
m
- the quantity of particles that make up an object
- scalar quantity
- measured in kilograms (kg)
weight
w
- the force due to gravity acting on an object
- w = mg
- measured in newtons (N)
lifts (elevator)
forces, energy, and power
- when an object is on a surface there are two forces acting on it: weight (w) and reaction force (R)
- a stationary lift gives the same result as a lift at a constant speed: R = w
- a lift accelerating upwards gives the same result as a lift deccelerating downwards: R > w
- a lift accelerating downwards gives the same result as a lift deccelerating upwards: R < w
inclined plane
forces, energy, and power
- when an object is on a slope, its weight acts downwards (towards the centre of the earth)
- since weight is a vector, the horizontal and vertical components can be calculated
- perpendicular to slope: F⊥ = wcosθ
- paralell to slope (force down the slope); F ∥ = wsinθ
work done
Ew
- a form of energy describing the force applied to move an object a certain distance
- Ew = Fd
gravitational potential energy
Ep
- the energy stored by an object as a result of its vertical position above the surface of a planet
- Ep = mgh
kinetic energy
Ek
- the energy possessed by a moving object
- Ek = 1/2mv2
conservation of energy
energy can not be created nor destroyed, but can change from one form to another
power
P
- the rate which energy is converted into other forms
- P = E/t
- power is measured in watts (W)
momentum
p
conservation of momentum
- the total momentum before a collision is equal to the total momentum after a collision in the absense of external forces
- p = mv
- m1u1 + m2u2 = m1v1 + m2v2
elastic collisions
- the kinetic energy before the collision is equal to the kinetic energy after the collision
- collisions between atoms, molecules, and sub-atomic particles are typically elastic
in-elastic collisions
- the kinetic energy before the collision is greater than the kinetic energy after the collision
- often during a collision energy is dissipated as heat, sound or in deforming materials
impulse
Ft
- impulse is equal to the change in momentum
- Ft = mv - mu
- dividing by ‘t’ shows that force is the rate of change in momentum
projectiles
- projectiles have a constant horizontal velocity and are accelerating vertically due to gravity
- for a projectile of velocity v at and angle of θ from the ground its horizontal velocity is vcosθ and its initial vertical velocity is vsinθ
satellites
a satellite is accelerating towards the earth due to gravity but is moving at a horizontal velocity such that it stays at a constant height above the earth, meaning it is in orbit
gravitational force of attraction
F
- F = Gm1m2/r2
- G, gravitational constant
- m1 and m2, mass of the objects
- r, distance between the two objects
r for a satellite above earth is hight of satellite + radius of earth
finding g from gravitational force of attraction
since F = w = mg, then rearrange equation to form:
g = Gm/r2
einsteins assumptions
special relativity
- the speed of light is absolute, it is always the same for all observers irrespective of their relative velocities
- the laws of physics are the same for all observers inside their frame of referance
time dialation
- if one observer is stationary, in that frame of referance, and the other is moving, the clock of the moving observer appears to be going slower than the clock of the stationary observer
- time slows, t’
- t’ = t/√1-(v/c)2
length contraction
- the decrease in length in the direction of motion of an object moving relative to a stationary observer
- length contracts, l’
- l’ = l√1-(v/c)2
light year
9.46x1015m
doppler effect
definition
the change in frequency and wavelength of a wave with respect to the velocity and direction of the source relative to an observer
doppler effect
frequency (formula)
fo = fs(v/v±vs)
redshift
z
- light is shifted towards the red end of the spectrum
- this occurs when a source in moving away from a stationary observer
- z = λo - λrest/λrest
- for slow moving galaxies z = v/c
blueshift
- light is shifted towards the blue end of the spectrum
- this occurs when the galaxy is moving towards a stationary observer
hubble’s law
- the red shift is directly proportional to the distance from the observer
- v = Hod
hubble’s constant
2.3x10-18 s-1
dark matter
- explains the recent estimate for the mass of the universe being much larger than visible matter
- its not mass as seen in stars and planets etc.
- its not dark clouds of normal matter
- its not antimatter (as gamma rays would be detected when antimatter annhialates matter)
- its not black holes as they have observable effects on light
dark energy
allows the explanation of the universes increasing expansion rate through energy we can not detect
measuring the heat of stars
- the energy emitted by stars is spread out over a large number of wavelengths
- there is a wavelength at which the star emits more energy than any other wavelengths, this is called the peak wavelength
- the peak wavelength is what is used to measure the temperature of the star
- the smaller the peak wavelength the higher the temperature of the star
universe expansion
proof
- cosmic microwave background radiation
- cosmological redshift
- olber’s paradox
olber’s paradox
if the universe is infinitely old, why is the night sky dark and not light?
- the fact it is dark means that the universe is not static and infinitely old but came into existance at a definite point in the past
- if the universe was static and there were infinite stars then any straight line from the earth should see a star and the sky would be light
- the universe is expanding, so light from distant galaxies is redshifted into obscurity
- the universe is young, so distant light has not reached earth yet
how to determine whether a collision is elastic or inelastic
- calculate the kinetic energy before and after the collision
- if kinetic energy is greater befor than after the collision is inelastic
- if the kinetic energy is equal then the collision is elastic