Science 30 Physics: Field Theory Topic 1: Gravitational Fields

Science 30 Physics: Field Theory

Topic 1: Gravitational Fields

Fields• A field is an invisible region of

influence that causes other objects to experience a force– What is a force?

• A push or pull • Fields can only be observed

indirectly through their effects on other objects

• We will study 3 types of fields:

1. Gravitational Field 2. Electric Field

3. Magnetic Field

Test object: Anything with mass

Test object: magnet

Test object: charged object (+)

+

Examples of gravitational fields: •Things falling to Earth •The Earth orbiting the sun

Examples of magnetic fields: •Magnets•Using a compass

Examples of electric fields: •Static electricity •Lightning

• A field line (or vector diagrams) tells us the direction and strength of a field – The direction of a field is determined by the direction a test object

will move

Gravitational Fields

Between Charges

An invisible region of influence where a force of attraction acts to pull a smaller object towards a larger more massive one

Remember gravity is an attractive force only. For example, an apple will fall towards the ground, but

WOULDN’T be repelled away from Earth.

What do you know about gravity?

Draw the gravitational field around earth. Where is the gravitational field strongest?

All objects with mass can produce a gravitational field, but an object

must be big enough to have observable effects

When compared to a smaller object, Earth’s gravitational field is always towards the earth itself

Both the sun and the Earth are capable of producing a gravitational field, but because the sun has a larger mass, Earth is attracted to and will orbit the sun. This is also the reason why the moon orbits Earth.

The gravitational field is strongest here

1. Gravitational Field Strength:

g = Gmr2

Gravitational Constant (__________________) kg

m

Equation is found on page 2 of the data booklet

• What happens to the gravitational field strength (g) if mass increases? _______________

• What happens to the gravitational field strength (g) if the radius increases? _______________

increase

decrease

Who will experience a higher GFS? A bird on the ground or a bird in the sky?

Practice using the equation by completing the graph on page 4.

Look up and write down what each variable means in your data booklet

6.67 x 10-11 Nm2/kg2

Magnitude of gravitational field strength (_______)N/kg

Mass of source (_________)

Radius or centre – to-centre distance (______)

How to use your data booklet correctly:

This is the formula

This is the formula

These are called variable (how we represent a

number or value)

These are called variable (how we represent a

number or value)

These are the units

for given variables These are the units

for given variables

Why do astronauts float in space? (click on picture to find out)

Defying Gravity?

If gravity pulls, why are objects able to on water float?

Does gravity act on helium balloons?

http://www.nasa.gov/mov/194279main_044_astronauts_float_in_space.mov

The shape of your graph is an exponential

decrease!

This is because we are dividing by a number

squared.

g = Gmr2

In science 30, you must be able to determine how mass and radius affect gravitational field strength. Use the following table along with the formula, g = Gm/r2, to work through what the new gravitational field strength would be.

g = Gmr2

If we look at the equation

Can G ever change? No, it’s a constant!

What happens if m increases?

g also increases since m is a numerator

What happens if r increases? g will decrease since r is a denominator (essentially we would be dividing by a larger number)

When we are asked to find the exact change to gravitational field strength (g) we can substitute in numbers.

For example, if mass is doubled we would substitute in m=2 into the equation. Anything that does not change will be given a value of 1. Take a look at some examples!

Because the mass of the object increases, we know that g will increase (Remember heavier objects have a greater g)

Increase

To find the change in g as a result of mass increase, we

will write the original equation.

g = Gm r2

Since the only change is mass and it is tripled, we put in 3 for m and then

write 1 for all other variables

g = (1)(3) (1)2

Solve

g = 3x

The new g is 3 times

the original

3 x 2 = 6 N/kg

Original gravitational field strength

(N/kg)

Change Will the gravitational field strength increase,

decrease, or stay the same

How much more or less will the gravitational

field strength be?

New gravitational field strength

(N/kg)

2 N/kg

Mass is tripled


(N/kg)




field strength be?


(N/kg)

2 N/kg

Mass reduced to 1/3

Because the mass of the object decreases, we know that g will decrease

Decrease

g = Gm r2

Since the only change is mass and it is reduced to 1/3 we put in 1/3 for m and then write 1 for all

other variables

g = (1)(1/3) (1)2

Solve

g = 1/3x

The new g is 1/3 the original

1/3 x 2 = 2/3 N/kg

Because the radius doubles, we are further from the object, we know that g will decrease

Decrease

g = Gm r2

Since the only change is radius and it doubles we

put in 2 for r and then write 1 for all other

variables

g = (1)(1) (2)2

Solve

g = ¼ x

The new g is 1/4 the original

¼ x 2 = ½ N/kg


(N/kg)




field strength be?


(N/kg)

2 N/kg

Radius is doubled

Because the radius is reduced, we are closer to the object, we know that g will increase

increase

g = Gm r2

Since the only change is radius and it is reduced

to 1/3 we put in 1/3 for r and then write 1 for all

other variables

g = (1)(1) (1/3)2

Solve

g = 9 xThe new g is 9 times

the original

9 x 2 = 18 N/kg

Be careful to remember to square the radius. (1/3)2 is 1/9.

Also always ask if you numbers match what you had originally predicted in the first part of the question

Which has a greater effect on g? radius or mass? Radius, since radius is squared in the equation


(N/kg)




field strength be?


(N/kg)

2 N/kg

Radius is reduced to 1/3

The middle! (Highlight this)

Practice converting units using page 1 of your data booklet

1. Convert 25 m to kilometer

2. Convert 500 km to meters

3. Convert 1400 nm to meters

4. Convert 42m to micrometers

25m = ________________km

10 3 Since we are moving out, we ÷÷

25 ÷ 103 = 0.025

500 km = ________________m

10 3 Since we are moving in, we Xx

500 X 103 = 500 000

1400 nm = ________________m

10 -9 Since we are moving in, we Xx1400 X 10-9 = 1.4 x 10-6

42 m = ________________µm 10 -6 Since we are moving out, we ÷÷

42 ÷ 10-9 = 4.2 x 107

Example: 1.Calculate the value of the gravitational field strength at the Earth’s surface. (Answer: 9.83 N/kg)

When no values are given, we use page 2 of the data booklet to find commonly used values.

Example: 1.Calculate the value of the gravitational field strength at the Earth’s surface. (Answer: 9.83 N/kg)

Find g

g = ?

Always list your variables so that you know what you are looking for and this helps you to stay organized!

m = 5.98 x 1024 kgr = 6.37 x 106 m

g = Gm r2

g = (6.67 x 10-11 Nm2/kg2)(5.98 x 1024 kg) (6.37 x 106 m)2

Canceling out units helps to make sure that your equation is correct!

9.83 N/kg

We should only have 3 sig digs!

g = 9.8298 N/kg

Assignment: Complete all the practice questions in the book. Practice makes progress and allows you to make mistakes before you get to an exam!

Example 1: Make sure your distance/radius (r) is converted to m (1km = 1000m). Also this is the distance including the radius of the Earth so we can use it as is without adding the radius of Earth.

For your pictures, make sure you draw the objects stated in the question as well as the direction of the field, similar to what we did on page 1 of the notes.

Example 2: Use the mass of the larger object that is producing the gravitational field.

Example 3: You must rearrange the formula to solve for m.

Example 4: You must rearrange the formula to solve for r.

m = gr2

G

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Science 30 Physics: Field Theory Topic 1: Gravitational Fields