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: A force? A push or a pull Gravitational Field 2. Electric Field 3. Magnetic Field

Examples of gravitational fields: Things falling to Earth The Earth orbiting the sun Examples of magnetic fields: Magnets Using a compass Test object: charged object (+) Test object: magnet Test object: Anything with mass + 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

What do you know about gravity? Gravitational Fields 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. Between Charges All objects with mass can produce a gravitational field, but an object must be big enough to have observable effects

Draw the gravitational field around earth. Where is the gravitational field strongest? When compared to a smaller object, Earth’s gravitational field is always towards the earth itself The gravitational field is strongest here All objects with mass can produce a gravitational field, but an object must be big enough to have observable effects   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.

g = Gm r2 1. Gravitational Field Strength: Look up and write down what each variable means in your data booklet 1. Gravitational Field Strength: Equation is found on page 2 of the data booklet Gravitational Constant (__________________) 6.67 x 10-11 Nm2/kg2 kg g = Gm r2 Mass of source (_________) Radius or centre – to-centre distance (______) Magnitude of gravitational field strength (_______) N/kg m 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.

How to use your data booklet correctly: This is the formula These are the units for given variables These are called variable (how we represent a number or value)

Defying Gravity? Why do astronauts float in space? (click on picture to find out) If gravity pulls, why are objects able to on water float? So how do astronauts float in space if the pull of gravity is so strong? Astronauts don't actually float. They are being pulled by the Earth's gravity just the same as the rest of us. But they are also orbiting the Earth, or moving sideways. This is known as centrifugal force. This sideways movement actually is pulling them away from the Earth at the same time that the Earth is pulling them down, so it appears as if they are floating. place When an object floats on the top of water, gravity is still in play. For an object to float, it must displace enough water to make up the same mass as the object itself. Once that happens, the remaining mass then sits on top of the water. For example: if a boat has a mass of 45 grams, it will displace 45 grams of water and if that has happened before the whole thing has sunk below the surface level of the water, the boat floats. Helium balloons are pulled by gravity, as are all objects with mass. The reason they don't fall is that there is another force acting on them, a buoyant force from air pressure that is equal to the weight of the air displaced by the balloon. Does gravity act on helium balloons?

g = Gm r2 The shape of your graph is an exponential decrease! This is because we are dividing by a number squared. g = Gm r2

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. If we look at the equation g = Gm r2 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!

2 N/kg Mass is tripled g = Gm r2 g = (1)(3) (1)2 g = 3x 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 g = Gm r2 g = (1)(3) (1)2 3 x 2 = 6 N/kg Increase g = 3x The new g is 3 times the original Because the mass of the object increases, we know that g will increase (Remember heavier objects have a greater g) To find the change in g as a result of mass increase, we will write the original equation. Since the only change is mass and it is tripled, we put in 3 for m and then write 1 for all other variables Solve

2 N/kg Mass reduced to 1/3 g = Gm r2 g = (1)(1/3) (1)2 1/3 x 2 = 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 reduced to 1/3 g = Gm r2 g = (1)(1/3) (1)2 Decrease 1/3 x 2 = 2/3 N/kg g = 1/3x Because the mass of the object decreases, we know that g will decrease 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 The new g is 1/3 the original Solve

2 N/kg Radius is doubled g = Gm r2 g = (1)(1) (2)2 g = ¼ x 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 Radius is doubled g = Gm r2 g = (1)(1) (2)2 ¼ x 2 = ½ N/kg Decrease g = ¼ x Because the radius doubles, we are further from the object, we know that g will decrease Since the only change is radius and it doubles we put in 2 for r and then write 1 for all other variables The new g is 1/4 the original Solve

Be careful to remember to square the radius. (1/3)2 is 1/9. 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 Radius is reduced to 1/3 g = Gm r2 g = (1)(1) (1/3)2 9 x 2 = 18 N/kg increase g = 9 x Because the radius is reduced, we are closer to the object, we know that g will increase The new g is 9 times the original 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 Solve 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 Radius, since radius is squared in the equation Which has a greater effect on g? radius or mass?

The middle! (Highlight this) Practice converting units using page 1 of your data booklet Convert 25 m to kilometer Convert 500 km to meters Convert 1400 nm to meters Convert 42m to micrometers 25m = ________________km 25 ÷ 103 = 0.025 The middle! (Highlight this) ÷ 10 3 Since we are moving out, we ÷ 500 km = ________________m 500 X 103 = 500 000 x 10 3 Since we are moving in, we X 1400 nm = ________________m 1400 X 10-9 = 1.4 x 10-6 x 10 -9 Since we are moving in, we X 42 m = ________________µm 42 ÷ 10-9 = 4.2 x 107 ÷ 10 -6 Since we are moving out, we ÷

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) g = Gm r2 g = ? m = 5.98 x 1024 kg r = 6.37 x 106 m 9.83 N/kg Find g g = (6.67 x 10-11 Nm2/kg2)(5.98 x 1024 kg) (6.37 x 106 m)2 g = 9.8298 N/kg We should only have 3 sig digs! Always list your variables so that you know what you are looking for and this helps you to stay organized! Canceling out units helps to make sure that your equation is correct!

Assignment: Complete all the practice questions in the book Assignment: Complete all the practice questions in the book. Practice makes progress and allows you to make mistakes before you get to an exam! 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 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. 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. m = gr2 G Example 4: You must rearrange the formula to solve for r.