Chapter 5 Gravity

Describing motion

• Speed: Rate at which object moves

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speed = distancetime

units of ms ⎛

⎝ ⎜

⎞

⎠ ⎟

example: 10 m/s

• Velocity: Speed and direction example: 10 m/s, due east

• Acceleration: Any change in speed or direction units: speed/time (m/s2)

• Constant velocity means a = 0

The Acceleration due to Gravity

• All falling objects accelerate at the same constant rate

• On Earth, g ≈ 10 m/s2: speed increases 10 m/s with each second of falling.

The Acceleration of Gravity (g)

• Galileo showed that g is the same for all falling objects, regardless of their mass.

Apollo 15 demonstration

Forces

• A force changes an object’s velocity

• A spinning or orbiting object has angular momentum: a force is required to change the rate of spin

There are usually lots of forces acting on an object.

Forces are caused by other objects.

An object can’t exert a force on itself!!

Newton’s Laws of Motion

1. Bodies at rest tend to stay at rest…

2. F = ma

3. Forces come in pairs: every action has an equal and opposite reaction:

Force that A exerts on B = force that B exerts on A

Weight vs. Mass• Weight is the force w = mg, directed toward the

center of the Earth

• The “normal force” is what a scale says

• Mass is a property of an object

• There is gravity in space

• “Weightlessness” = scale reads 0

• due to a constant state of free-fall

Why are astronauts ‘weightless’ in space?

Conservation of Momentum

• The total momentum of interacting objects cannot change unless an external force acts on them

• Interacting objects exchange momentum through equal and opposite forces

What keeps a planet rotating, and orbiting the Sun?

Conservation of Angular Momentum

• The angular momentum of an object cannot change unless a force acts on it

• Earth’s rotation and orbit will continue (almost) forever because it can’t “get rid of” angular momentum

angular momentum = mass x velocity x radius of orbit

Conservation of angular momentum

Total Energy is conserved

• Kinetic (motion)• Radiative (light)• Stored or potential

Energy can easily change type but cannot be destroyed.

Professor Kress:Ive read all of 5.1 and can't get the answer for number 2.so far i checked-The acceleration due to gravity near Earth’s surface is 9.8 m/s2.-The speed of falling objects increases at a constant rate.-Objects tend to slow down naturally unless propelled by a force. These ones are hard!!

1. The acceleration due to gravity near Earth’s surface is 9.8 m/s2

2. Inertia is an object's tendency to resist changes in its motion.3. The speed of falling objects increases at a constant rate.4. Galileo's experiments yielded similar results to Aristotle's

theories about motion.5. The speed of a falling object depends on its weight.6. According to tradition, Galileo dropped objects of different

mass from the leaning tower of Pisa.7. Objects tend to slow down naturally unless propelled by a

force.

Homework problem #2

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Homework problem #3: A student sent me this….

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Homework problem #3

Newton’s Universal Law of Gravitation:1. Every mass attracts every other mass.2. Attraction is directly proportional to the product of

their masses.3. Attraction is inversely proportional to the square of

the distance between their centers.

d

M1

M2

F = G M1 M2

d2

Newton’s Version of Kepler’s Third Law

p = orbital period

a=average orbital distance (between centers)

(M1 + M2) = sum of object masses, relative to

Sun (Solar masses)

a3

p2= M1 + M2

Now we see why orbital period does not depend on the mass of the planet!

Kepler’s 2nd Law explained

• Total orbital energy (gravitational + kinetic) stays constant if there is no external force

• Orbits cannot change without help from an outside object

• Conservation of angular momentum!

More gravitational energy;Less kinetic energy

Less gravitational energy;More kinetic energy

Total orbital energy stays constant

Thought Question:Which has a total force of 0?

1. A car rolling to a stop.

2. A rock freely falling through the air.

3. A skydiver moving at terminal velocity.

4. A bicycle going around a curve at constant speed.

5. A moon orbiting Jupiter.

On the Moon:

A. My weight is the same, my mass is less.

B. My weight is less, my mass is the same.

C. My weight is more, my mass is the same.

D. My weight is more, my mass is less.

If you jump out of a plane without a parachute:

A. My weight is the same, my mass is zero.

B. My weight is zero, my mass is the same.

C. My weight is more, my mass is the same.

D. My weight is more, my mass is zero.

E. My mass and weight are both zero.

a. Their mass has become zero.

b. The astronauts are so far from Earth, they don’t feel Earth’s gravity

c. The Moon pulls on them in the opposite direction as Earth, balancing out

d. They are actually in free-fall

Why are astronauts weightless in space?

Thought Question:Is the force the Earth exerts on you larger, smaller,

or the same as the force you exert on it?

A. Earth exerts a larger force on you.

B. I exert a larger force on Earth.

C. Earth and I exert equal and opposite forces on each other.