Gravitational Fields

IB Physics Power Points

Topic 6 SL

Fields and Forces

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Defining Mass

Inertial mass

inertial

Fm

a

A measure of an object’s inertia (tendency to resist a change in motion)

The property of matter that gives rise to the gravitational attraction between objects.

The gravitational force is proportional to the product of the two object’s masses.

Gravitational mass

Expressed as a ratio of net force and acceleration – Newton’s 2nd Law

Newton’s Universal Law of Gravitation

Consider – two masses A and B

1 22

mm

F Gr

This gravitation attraction can be calculated by

There is a gravitational attraction between A and B.

FB on A = - FA on B (think Newton’s 3rd)

The gravitational constant G = 6.67×10-11 N m2 kg-2

The gravitational force is:

Proportional to the product of the two masses.

Inversely proportional to the square of the distance between the center of mass of each object.

NULOG “an inverse square law”

How could we determine G experimentally?

Practice: Find the gravitational force of attraction between a 75 kg physics student and her 1 500 kg car when their centers are 10.0 m apart.

A. 7.5 x10-8 NB. 7.5 x10-7 NC. 740 ND. 1.5 x103 N

Falling objects and the force of gravity

Free-body diagrams and elevators – what do scales measure?

Draw free body diagrams (including annotations and calculated values) representing the following situations (consider g = 10 ms-2)

i. A 50 kg student in an elevator at restii. A 50 kg student in an elevator moving

downwards at 2 ms-1.iii. A 50 kg student in an elevator moving

upwards at 5 ms-1.iv. A 50 kg student in an elevator

accelerating upwards at 1 ms-2.v. A 50 kg student in an elevator

accelerating downwards at 3 ms-2

vi. A 50 kg student in an elevator falling freely

Consider an object (mass m) at some point P, in the Earth’s gravitational field.

The object will feel a force (Fe) that can be calculated using:

2e

e

m mF G

r

2e

e

m mF G

r

Gravitational Field Strength

Defined – the force per unit mass acting on an object placed in a gravitational field.

In the example, the force on the object at point P in the Earth’s gravitational field can be calculated by:

Fg

m

So by substitution

2

2

MmGF Mrg G

m m r

The gravitational field strength (FORCE PER UNIT MASS) at distance r from the center of mass M (the object creating the gravitational field)

At the surface of a planet (like Earth), the gravitational field strength can be determined by:

2

0 2

MmGF Mrg G

m m r

Where M is the mass of the planet. For Earth:

2E

E

Mg G

r

Given

Earth’s mass: 5.97 x 1024 kg

Earth radius: ~ 6.38 x 103 km

Determine a value for the gravitational field strength at the Earth’s surface.

Gravitational Fields

Gravity is a field force. It exists between objects without contact and cannot be shielded or blocked.

Gravitational fields are depicted by drawing field diagrams. Field lines show the direction of the force acting on a particle placed in the field (toward the center of mass)

The density of field lines indicates the strength of the field.

Gravitational Field Strength – More than one point mass

Consider the following diagram and determine the gravitational field strength at point P, located 3.45 x 108 m from the centre of the Earth.

Moon mass: 7.35 x 1022 kgEarth-Moon distance: 384 x 103 km

The gravitational fields of the earth and moon superpose.

Note how the fields cancel at one point, and how there is no boundary between the interpenetrating fields surrounding the two bodies.