12: The Gravitational Field Flashcards by Elaine O'Brien

What is angular velocity?

The angle the object rotates through per second

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what is the circular motion of an object

object moving in a circle with constant acceleration towards the centre

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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

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In which direction is a car travelling in a circle, accelerating?

Centripetal acceleration is always directed towards the centre of the circle

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What produces the centripetal acceleration and what does it do

Centripetal force, the force which acts at right angles to the direction of motion

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In which direction does centripetal force act?

Towards the centre of the circle

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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

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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

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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.

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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

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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

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What does an object experience when you put it in a gravitational field of another object?

Experience an attractive force

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What are gravitational field lines?

Arrows showing the direction of the force that masses would feel in a gravitational field of another object

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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

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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

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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

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Why does a small mass in earth’s gravitational field not affect earth much?

Earth is so much more massive

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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

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The force experienced by an object in a gravitational field is always []

Attractive

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What is gravitational field strength g?

Force per unit mass

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A mass in a uniform gravitational field experiences a [] force

constant - because g will be the same everywhere

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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