12: The Gravitational Field Flashcards
What is angular velocity?
The angle the object rotates through per second
what is the circular motion of an object
object moving in a circle with constant acceleration towards the centre
Why is a car travelling at constant speed in a circle, accelerating?
It’s velocity is changing since its direction is changing And acceleration = rate of change of velocity
In which direction is a car travelling in a circle, accelerating?
Centripetal acceleration is always directed towards the centre of the circle
What produces the centripetal acceleration and what does it do
Centripetal force, the force which acts at right angles to the direction of motion
In which direction does centripetal force act?
Towards the centre of the circle
what does the equation a = v^2 / r give and what type of acceleration is this what is v
the constant acceleration of an object towards the centre of the circle this is centripetal acceleration v is linear velocity
what is the equation F = mv2 / r for, what does it give
this is the equation for centripetal force, the force keeping an object in circular motion
why does linear velocity of particles increase as they spiral outwards, even though angular velocity is constant
v = r ω, ω stays constant but as the particle spirals outwards, r increases and so does v because of it.
why don’t we notice the spin of the Earth
our centripetal accel is so small and everything including us is moving at the same speed
What is a gravitational field?
A region where an object will experience a non-contact force, an attractive force to the object whose gravitational field it’s in
What does an object experience when you put it in a gravitational field of another object?
Experience an attractive force
What are gravitational field lines?
Arrows showing the direction of the force that masses would feel in a gravitational field of another object
What is a uniform field? How can you identify a uniform field with field lines?
A field that is the same everywhere. This is shown by the field line being equally spaced and going in the same direction
Point masses have a [] field (Point masses = ….)
Radial A mass where its assumed they act as if all there mass in concentrated at their centre
As a mass gets further from earth, what happens to the strength of the force it experiences? How is that represented in field lines?
Further - force decreases Lines of force are further apart
Why does a small mass in earth’s gravitational field not affect earth much?
Earth is so much more massive
What can you assume about the gravitational field at the surface of Earth? How is this represented in field lines?
Assume it is perfectly uniform So the field lines are parallel and equally spaced
The force experienced by an object in a gravitational field is always []
Attractive
What is gravitational field strength g?
Force per unit mass
A mass in a uniform gravitational field experiences a [] force
constant - because g will be the same everywhere
what do gravitational field lines that are closer together signify
at those points the gravitational field is stronger
When is ΔEɢᵣₐᵥ positive? Negative?
what is ΔEɢᵣₐᵥ the same as
Positive: When the height increases Neg: When the height decreases
ΔEɢᵣₐᵥ = mgh (gravitational potential energy)
What is the principle of conservation of energy?
Energy cannot be created or destroyed. Energy can be transferred from one form to another but the total amount of energy in a closed system will not change
You [] gravitational potential energy if you move away from the Earth
why
Gain
ΔEɢᵣₐᵥ = mgh
g and h don’t change but your h, height so distance from earth increases so you gain GPE
Egrav is always positive/negative
Negative (always attractive)
What is a satellite?
A small mass that orbits a much larger mass
When something is in orbit, which 2 forces must be equal? and how can you use this to find velocity of mass in orbit
Centripetal force and gravitational force mv²/r = GmM/r²
mv² = GmM / r
v² = GM / r
v = SQR (GM / r)
what does an object, like the earth, with a radial field (component) mean
anything with a radial field (component) has its lines of force meeting at the centre of the object that it’s attracted to, so lines of force go into the centre of the Earth from other objects
what is g
g is the acceleration due to gravity of a mass directed at the center of the attracting mass
principle of the conservation of energy
energy cannot be created or destroyed. energy can be transferred from one store to another, but will not change in a closed system.
equation for kinetic energy
1/2mv²
equation for change in change in gravitational potential energy
mgh
how to show conservation of energy between kinetic energy and gravitational potential energy
1/2mv² = mgh
What is gravitational potential?
Potential energy per unit mass
what is an equipotential
example of something containing equipotentials
an area in which field lines are parallel, meaning there’s a constant gravitational potential.
a uniform field contains equipotentials
What do equipotentials show?
All the point in a field which have the same potential
If you travel along a line of equipotential you don’t lose or gain [],
GPE only changes when moving up and down []
so it doesn’t matter what [] an object takes
the [] is the same as long as
it moves the same []
GPE - no work is done
field lines
path
change in GPE
vertical distance
show thtat change in GPE is 0 when moving along equipotentials
change in energy = electric Force * distance Fgrav * S
Fgrav * 0 = 0
electric force acting along equipotential = 0
0 change in GPE
What shape are the equipotentials around a uniform spherical mass?
Spherical surfaces
features of graph of distance r versus Fgrav, Vgrav, E and g
all the graphs are below the x axis only touching the x-axis at at infinity r
they are all below the x-axis as gravity is an attractive force signified by a negative sign
relationship between Fgrav, g, Egrav and Vgrav
you get the area under Fgrav to get Egrav
you get the gradient of Egrav to get Fgrav
you get the area under g to get Vgrav
you get the gradient of Vgrav to get g
what does the area under a graph of g (grav field strength) against distance give
The area under the field strength (g) graph is equal to the change in gravitational potential Vgrav
what does area under a graph of gravitational force Fgrav against distance give?
The area under a Fgrav graph is equal to the change in potentia; gravitational potential energy Egrav
what does the gradient of gravitation potential energy E against distance r give
the gradient of the Eelectric (GPE) graph is equal to the fgrav.
what does the gradient of the graph of gravitational potential g against distance r give
The gradient of the Vgrav graph is equal to gravitational field strength g
in what directions does the gavitational potential energy change
Gravitational potential energy does not change when moving along field lines, only when moving up or down. Therefore, no matter what path an object takes, the energy change is the same as long as it moves the same vertical distance.
what is newton’s law of gravitation
all particles with mass attract all other particels
how to calculate radius of orbit of satellite
force providing centripetal acceleration mv² / r = GMm / r² gravitational force on satellite
divide by m: v² / r = GM / r²
multiply by r: v² = Gm / r
also, v = 2πr / t the speed of the satellite in orbite
so v² also = 4πr² / T²
GM / r = 4πr² / T²
GM = 4πr³ / T²
GMT² / 4π² = r³
r = CUBE ROOT (GMT² / 4π²)
how to calculate change in GPE Egrav when moving a mass between 2 distances
work is done against the force of gravity
work done depends on force and distance moves
Egrav = Fgrav * s
total gravitational potential energy of a satellite
Egrav = Egravtotal - kinetic energy
what energy does a spacecraft need to make it out of earth’s potential well
use this to find escape velocity
its kinetic energy must be greater than its gravitational potential energy because GPE is negative, but it needs energy more than or equal to 0
Ekinetic + Epotential >= 0
1/2mv² + (-)GMm/r >= 0
Vesc = SQR (2GM / r)
constant speed, force of gravity, gpe
Fgrav and GPE are negative, F is attractive force so its in the opposite direction to a mass trying to leave earth, Earth is in a potential well, so GPE is negative, less negative as you try escape earth
circular orbit has constant r so gravitational force is constantly at right angles to velocity so speed doesn’t change
orbit follows a gravitational potential so gpe is constant
elliptical orbit r constantly changing so gravitational force constantly changing, comet rises and falls in sun’s potential well increasing gpe when further away like at B2 and so losing Ke, so speed cannot be constant
draw a triangle
adjact line going up with 26klight years, the angle the comet would move through from 0 microrad to -1 microrad is an angle of 1microradian, opposite side at top gives you the radius of the orbit
tan(1*10-6) * 26000 * 9.5 * 1015 = 2.47 * 1014m
