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Physics A - Level > Fields (1): Gravitational Fields > Flashcards

Fields (1): Gravitational Fields Flashcards

1
Q

What is the definition of a gravitational field?

A

The region of space around a mass where other bodies placed in it will feel a force of attraction towards it

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2
Q

What is the definition of a field line/line of force?

A

The path in which a mass will follow if placed in a strong enough field to move it

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3
Q

What happens when a small mass and large mass are placed close to one another?

A

The small mass and large mass attract each other with equal and opposite forces. However, since the force is too small to move the large mass noticeably the small mass is pulled by the force to the large mass.

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4
Q

What is the definition of gravitational field strength, g?

A

The force per unit mass on a small test mass when placed in a field

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5
Q

Why does the test mass need to be small when measuring the gravitational field strength?

A

As otherwise it might pull so much on the other object that it changes its position and alters the field.

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6
Q

What is the equation for gravitational field strength on a test/point mass at a particular point in a uniform field?

A

g = F/m

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7
Q

What are the units for gravitational field strength?

A

Nkg^-1

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8
Q

Does the force on a test mass in a gravitational generally vary as it is moved from one position to another?

A

yes

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9
Q

If an object is in a field and experiences no other forces apart form gravity, what is its acceleration equal to? What equation proves this?

A

acceleration = g

a = F/m (using F=ma)
a = mg/m (using F=mg)
a=g

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10
Q

What term would you use to describe an object in a field that is only acted upon by gravity?

A

the object is unsupported so it falls freely

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11
Q

How does the magnitude of g vary in a radial field?

A

Decreases with increasing distance from the massive body

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12
Q

How does the magnitude of g vary in a uniform field?

A

Constant in magnitude and direction throughout the field

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13
Q

Describe the field lines of a radial field?

A
  • Field lines are like spokes pointing to the centre of the spherical object
  • Any object in this field will experience a force pointing to the centre to the massive object

NB: At the surface of a large spherical object e.g earth, the field is uniform

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14
Q

Describe the field lines of a uniform field?

A
  • Field lines are parallel and equidistant from one another
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15
Q

For a free falling object, does the acceleration of it depend on its mass?

A

No, as a=g (independent of m)

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16
Q

What is the equation for gravitational field strength on a test/point mass at a particular point in a radial field?

A

g = GM/r^2

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17
Q

Where does gravity act?

A

On any object with mass

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18
Q

What is gravity always?

A

Attractive

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19
Q

What is the equation for the force on a test mass, m that is in a radial field at a distance of r from the spherical mass’ centre?

A

F=GMm/r^2

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20
Q

How do you get from the equations for gravitational field strength to the equation for the force on

A

g = F/m = GM/r^2

F =GMm/r^2

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21
Q

What does Newtons law of Gravitation show us?

A

That the field of a spherical mass is that same as if the mass were concentrated at its centre

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22
Q

What does r stand for in the F=GMm/r^2 equation?

A

The distance of the test mass form the centre of the spherical mass

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23
Q

What is the definition of gravitational potential energy?

A

The energy of an object due to its position in a gravitational field

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24
Q

What are the units of gravitational potential energy?

A

Joules, J

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25
Q

At what point in the universe is GPE = 0?

A

At infinity - the object is so far away that the gravitational force is negligible

26
Q

What do objects need to do to escape from a gravitational field?

A

Do work against the force of gravity on it due to the planet

27
Q

What is the definition of gravitational potential, V, at a point in a field?

A

The work done per unit mass to move a small test mass from infinity to that point/ the GPE per unit mass of the small test mass

28
Q

What sign are GPE values?

A

-ve

29
Q

What is the equation for GPE?

A

-GMm/r

30
Q

How do you get from the equation for force in a radial field to the equation for GPE?

A

W = Fd
W = Fr
F = W/r

F = GMm/r^2
W/r = GMm/r^2
W = GMm/r

NB: -ve because GPE’s are always negative

31
Q

How do you calculate the speed required to leave the field of a massive object using GPE?

A

GPE = -KE
KE = 1/2mv^2

32
Q

What is the equation for the gravitational potential at a distance r from the centre of a spherical mass?

A

V = -GM/r

33
Q

What is the equation for the work that must be done for a mass, m, to escape from from a gravitational potential,V?

A

W = mV

34
Q

What is the equation for the work done required to move a mass, m, from one gravitational potential to another?

A

(delta)W = m(delta)V

(delta)V = (V2 - V1)

35
Q

What is the definition of an equipotential?

A

Surfaces/lines of constant potential

36
Q

What is a key feature of equipotentials?

A

No work is done to move along an equipotential surface

37
Q

What does the density of field lines show you?

A

The strength of the field at that point

38
Q

How are equipotentials drawn?

A

perpendicular to field lines

39
Q

What is the definition of potential gradient?

A

The change in potential per metre at that point

40
Q

What is the equation for potential gradient?

A

(delta)V/ (delta)r

41
Q

What is the equation for gravitational field strength as defined by the potential gradient?

A

-(delta)V/ (delta)r

42
Q

What is Keplers third law?

A

r^3/T^2 is the same for all planets

T^2 is proportional to r^3

43
Q

What did Newtons law of Gravitation find?

A

The gravitational force between two point objects is:
- Always attractive
- proportional to the mass of each object
- proportional to 1/r^2, where r is there distance apart

44
Q

What is G and what is its value?

A

The universal constant of gravitation, 6.67 x 10^-11Nm^2kg^2

45
Q

Instead of saying separation between 2 objects, what vocabulary should you use instead?

A

Distance between centres or distance between surfaces

46
Q

What is the volume of a sphere?

A

4/3(pi)r^3

47
Q

What is the inverse square law?

A

That gravitational field strength/force decreases by 1/r^2/ with inverse proportion to r^2

48
Q

How do you prove the inverse square law?

A

g = GM/r^2

gravitational field strength on the surface of the spherical body:

g(s) = GM/R^2
GM = g(s)R^2

where R is radius of the spherical body

g = g(s)R^2/r^2

at distance r=2R
g = g(s)R^2/(2R)^2 = g(s)/4

at distance r=3R
g = g(s)R^2/(3R)^2 = g(s)/9

at distance r=4R
g = g(s)R^2/(4R)^2 = g(s)/16

49
Q

Describe the graph of gravitational field strength against distance from the centre of a planet with the radius R?

A
  • From 0 to R the gravitational field strength increases proportionally to g(s) (which is the maximum)
  • From R -> 2R -> 3R the gravitational field strength decreases following the inverse square law
50
Q

Why does g decrease as you go from the surface of a spherical planet to its centre?

A

You are decreasing both r^2 and the M (mass) that you are accounting for - any mass outside the radius gives no resultant force

51
Q

What is the definition of escape velocity?

A

The minimum velocity an object must be given to escape from the planet when projected vertically from the surface

52
Q

What is the equation for escape velocity?

A

vesc = root(2GM/R)
vesc = root(2gR)

53
Q

For an object projected at a speed, v, what does its kinetic energy need to be greater than or equal to?

A

(delta)W

54
Q

What is the equation for centripetal acceleration?

A

a = v^2/r

55
Q

How can you determine the velocity of planet using gravitational field strength?

A

Equate g and centripetal acceleration

GM/r^2 = v^2/r
GM/r = v^2

where M is the mass of the sun

56
Q

What is the calculation proof of Keplers Law?

A

v = 2(pi)r/T

GM/r = (2(pi)r)^2/T^2

rearrange
r^3/T^2 = GM/4(pi)^2

since GM/4(pi)^2 is the same for all planets so is r^3/T^2

57
Q

When you calculate values of r using equations, what do you need to make sure to do?

A

minus the value of the radius of the spherical object

58
Q

What is the definition of a geostationary satellite?

A

A satellite that orbits the earth directly over the equator and has a time period of 24hrs

59
Q

How do you find the height of a geostationary satellite above a planet?

A

r^3 = GMT^2/4(pi)^2

where T is the time period of the planet

60
Q

The total energy of an orbiting satellite is…?

A

gravitational potential energy + kinetic energy

61
Q

What is the equation for the energy of an orbiting satellite?

A

KE = 1/2mv^2 = 1/2m(GM/r) = GMm/2r

GPE = -GMm/r

GPE + KE = -GMm/2r

62
Q

What is the definition of a geosynchronous satellite?

A

Satellites that have an orbital period the same as earths rotational period

Physics A - Level (24 decks)

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