# Lesson 12: Title: Gravity (May Take Two Days)

Nelson Text: p82-95 Date: Feb 2003

Course: SPH 3U1

Unit: MECHANICS

## Lesson 12: Title: Gravity (may take two days)

Bellwork: Draw an FBD of an airplane flying at 300 km/hr at 1500 m.

and of a toboggan sliding down a slope

p 121 #1

**May want to do this before FBD's so that you can include Fg and Fn in FBDs?**

Preliminaries: return labs, collect assignments

demos of Newton's laws (no time for this in this long lesson)

Lesson:

Pretest: (1) What is gravity? (2) What causes gravity? (3) What determines how fast things fall?

Discuss how the various ideas can be tested. Why might people think that particular idea?

Definition:

Gravity is caused by matter. All matter has mass. All mass is attracted to all other mass. We call this attractive force “gravity”.

** (If not discussed above: Is there any way to test this definition? Why might someone think this? Are there observations that it cannot explain?)*

What makes gravity stronger? weaker?

Gravity is stronger when masses are bigger and weaker when they are further apart.

Which is bigger? the earth or the moon? [How do you know?]

\ we weigh more on earth than on the moon.

What are tides caused by? [How do you know?]

Jupiter is much bigger than the moon [how do you now?], but much farther away. \ it doesn’t have enough influence to cause tides.

Sir Isaac Newton investigated these things, and **discovered the Law of Universal Gravitation:**

This tells us the force of gravity between two masses m1 and m2 that are separated by a distance d (sometimes also called r). Note that d is measured from the centre of each mass.

G is the universal gravitational constant, a fundamental constant of the universe (like the speed of light). G=6.67 E-11 *What do you notice about this number?*

What units must it have? Nm2/kg2

This is not a vector equation. So, in which direction does gravity act? It pulls things towards each other.

Example: What is the force of gravity between the earth and a 100 kg satellite 200 km above the earth’s surface? **Draw a FBD first**. (*indicate that the force of gravity on each one is equal and opposite)*

.....

What is the force of gravity on a mass m that is resting on the earth’s surface?

Fg = (6.67 E-11 Nm2/kg2 ) (m)(5.98E24 kg)

------

(6370,000 m)2

= m (9.8 N/kg)

The force of gravity on a mass m at the earth’s surface is m x (9.8 N/kg) . We call this number ‘g’, the **gravitational field intensity**. (as long as you don’t change me or re ) \ Fg = mg.

NOTE that the units N/kg are the same as m/s2 , however we can’t just write -9.8 m/s2 because an object that is not accelerating, but at rest on a table still experiences a force of gravity. It only accelerates at 9.8m/s2 once it is dropped.

**Which will fall faster**, this paper ball or this textbook? Why? - drop both! What did you see?

**What determines how fast something falls?**

(i) the force of gravity, (ii) air resistance (this depends on shape, mass, speed, and type of fluid).

For something falling in a vacuum, the only force on it is Fg. \ Fnet = Fg, or ma = mg. \ag = g .

So the acceleration due to gravity on any mass near the surface of the earth is -9.8m/s2 !!! This means that all masses accelerate at the same rate - the mass does not matter! This is why we did not ever include the mass in our equations of motion (d=1/2at2+v1t+d1 and v=at+v1 ). Any object dropped from height h will reach the ground at the same time. (Use kinematic equations to figure it out: h = 1/2gt2 so t = Ö2h/g . )

What is the difference between **mass and weight?**

Mass is

· a measure of the amount and type of matter in an object.

It doesn’t change unless you change the object.

· Units: kilograms.

· Measured on a balance. (diagram and explain why it reads the same under any gravitational field)

Weight is

· the same as the force of gravity on an object. W = |Fg|.

No gravity = no weight! but you still have mass.

· Units: Newtons.

· Measured on a spring scale. (diagram and explain why it reads differently on a different planet).

Orbits - go over Newton’s idea of a cannon on a hill à satellite in orbit. bigger orbit = more speed.

Weightlessness in orbit? No, you are not weightless. There is still a force of gravity on you, although a spring scale would not measure it (neither would a balance) because both you and the scale are falling. Instead of weightlessness, we say “free fall”. Imagine Newton’s cannonball falling – about to hit the earth – but it doesn’t – because the earth curves down away before the cannonball gets to it. The cannonball keeps falling towards the earth and the earth keeps curving away.

See webphysics.ph.msstate.edu/javamirror/ntujava/Default.htm

Choose Dynamics #3: "Projectile/Satellite Orbits" - work though this example

There is still gravity, you just don’t feel it because you are always falling around the earth.

(** can you prove that if an object in orbit increases speed then it will move to a larger orbit?)

Homework:

I. p93#1-4, p96 #1,2Nelson: p85ff #4, 6, 10, p90#10, p93#4 p95#6

(discuss p95#7 – how satellites stay in right orbit)

II. Calculate the force of gravitational attraction between a boy and a girl, each massing 60 kg, 1m apart. 1 mm apart? impossible -- (i) masses not concentrated at one point (ii) cannot get centres of mass 1 mm apart.

III. a) List two ways to reduce the weight of an object.

b) List one way to reduce the mass of an object.

Evaluation:

Yep it is a long lesson! – there is time on the second day to work on homework.

Also need to discuss inverse square laws. see page 91

and the normal force?

*Normal Force: - leave for when you do force problems.*

Typically, on a horizontal surface, if there are no other vertical forces.

Do an example of a weight hanging from an elastic on a surface. Find FN