12: The Gravitational Field

Question 1

What is angular velocity?

Answer 1

The angle the object rotates through per second

Question 2

what is the circular motion of an object

Answer 2

object moving in a circle with constant acceleration towards the centre

Question 3

Why is a car travelling at constant speed in a circle, accelerating?

Answer 3

It’s velocity is changing since its direction is changing And acceleration = rate of change of velocity

Question 4

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

Answer 4

Centripetal acceleration is always directed towards the centre of the circle

Question 5

What produces the centripetal acceleration and what does it do

Answer 5

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

Question 6

In which direction does centripetal force act?

Answer 6

Towards the centre of the circle

Question 7

what does the equation a = v^2 / r give and what type of acceleration is this what is v

Answer 7

the constant acceleration of an object towards the centre of the circle this is centripetal acceleration v is linear velocity

Question 8

what is the equation F = mv2 / r for, what does it give

Answer 8

this is the equation for centripetal force, the force keeping an object in circular motion

Question 9

why does linear velocity of particles increase as they spiral outwards, even though angular velocity is constant

Answer 9

v = r ω, ω stays constant but as the particle spirals outwards, r increases and so does v because of it.

Question 10

why don’t we notice the spin of the Earth

Answer 10

our centripetal accel is so small and everything including us is moving at the same speed

Question 11

What is a gravitational field?

Answer 11

A region where an object will experience a non-contact force, an attractive force to the object whose gravitational field it’s in

Question 12

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

Answer 12

Experience an attractive force

Question 13

What are gravitational field lines?

Answer 13

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

Question 14

What is a uniform field? How can you identify a uniform field with field lines?

Answer 14

A field that is the same everywhere. This is shown by the field line being equally spaced and going in the same direction

Question 15

Point masses have a [] field (Point masses = ….)

Answer 15

Radial A mass where its assumed they act as if all there mass in concentrated at their centre

Question 16

As a mass gets further from earth, what happens to the strength of the force it experiences? How is that represented in field lines?

Answer 16

Further - force decreases Lines of force are further apart

Question 17

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

Answer 17

Earth is so much more massive

Question 18

What can you assume about the gravitational field at the surface of Earth? How is this represented in field lines?

Answer 18

Assume it is perfectly uniform So the field lines are parallel and equally spaced

Question 19

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

Answer 19

Attractive

Question 20

What is gravitational field strength g?

Answer 20

Force per unit mass

Question 21

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

Answer 21

constant - because g will be the same everywhere

Question 22

what do gravitational field lines that are closer together signify

Answer 22

at those points the gravitational field is stronger

Question 23

When is ΔEɢᵣₐᵥ positive? Negative?

what is ΔEɢᵣₐᵥ the same as

Answer 23

Positive: When the height increases Neg: When the height decreases

ΔEɢᵣₐᵥ = mgh (gravitational potential energy)

Question 24

What is the principle of conservation of energy?

Answer 24

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

Question 25

You [] gravitational potential energy if you move away from the Earth

why

Answer 25

Gain

ΔEɢᵣₐᵥ = mgh

g and h don’t change but your h, height so distance from earth increases so you gain GPE

Question 26

Egrav is always positive/negative

Answer 26

Negative (always attractive)

Question 27

What is a satellite?

Answer 27

A small mass that orbits a much larger mass

Question 28

When something is in orbit, which 2 forces must be equal? and how can you use this to find velocity of mass in orbit

Answer 28

Centripetal force and gravitational force mv²/r = GmM/r²

mv² = GmM / r

v² = GM / r

v = SQR (GM / r)

Question 29

what does an object, like the earth, with a radial field (component) mean

Answer 29

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

Question 30

what is g

Answer 30

g is the acceleration due to gravity of a mass directed at the center of the attracting mass

Question 31

principle of the conservation of energy

Answer 31

energy cannot be created or destroyed. energy can be transferred from one store to another, but will not change in a closed system.

Question 32

equation for kinetic energy

Answer 32

1/2mv²

Question 33

equation for change in change in gravitational potential energy

Answer 33

mgh

Question 34

how to show conservation of energy between kinetic energy and gravitational potential energy

Answer 34

1/2mv² = mgh

Question 35

What is gravitational potential?

Answer 35

Potential energy per unit mass

Question 36

what is an equipotential

example of something containing equipotentials

Answer 36

an area in which field lines are parallel, meaning there’s a constant gravitational potential.

a uniform field contains equipotentials

Question 37

What do equipotentials show?

Answer 37

All the point in a field which have the same potential

Question 38

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 []

Answer 38

GPE - no work is done

field lines

path

change in GPE

vertical distance

Question 39

show thtat change in GPE is 0 when moving along equipotentials

Answer 39

change in energy = electric Force * distance Fgrav * S

Fgrav * 0 = 0

electric force acting along equipotential = 0

0 change in GPE

Question 40

What shape are the equipotentials around a uniform spherical mass?

Answer 40

Spherical surfaces

Question 41

features of graph of distance r versus Fgrav, Vgrav, E and g

Answer 41

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

Question 42

relationship between Fgrav, g, Egrav and Vgrav

Answer 42

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

Question 43

what does the area under a graph of g (grav field strength) against distance give

Answer 43

The area under the field strength (g) graph is equal to the change in gravitational potential Vgrav

Question 44

what does area under a graph of gravitational force Fgrav against distance give?

Answer 44

The area under a Fgrav graph is equal to the change in potentia; gravitational potential energy Egrav

Question 45

what does the gradient of gravitation potential energy E against distance r give

Answer 45

the gradient of the Eelectric (GPE) graph is equal to the fgrav.

Question 46

what does the gradient of the graph of gravitational potential g against distance r give

Answer 46

The gradient of the Vgrav graph is equal to gravitational field strength g

Question 47

in what directions does the gavitational potential energy change

Answer 47

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.

Question 48

what is newton’s law of gravitation

Answer 48

all particles with mass attract all other particels

Question 49

how to calculate radius of orbit of satellite

Answer 49

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)

Question 50

how to calculate change in GPE Egrav when moving a mass between 2 distances

Answer 50

work is done against the force of gravity

work done depends on force and distance moves

Egrav = Fgrav * s

Question 51

total gravitational potential energy of a satellite

Answer 51

Egrav = Egravtotal - kinetic energy

Question 52

what energy does a spacecraft need to make it out of earth’s potential well

use this to find escape velocity

Answer 52

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)

Question 53

Answer 53

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

Question 54

Answer 54

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