1. Chapter 4 Making Sense of the Universe:
Understanding Motion, Energy, and Gravity

2. Describing Motion Speed: How Fast.
Velocity: How fast in which direction.
Acceleration: How fast and in which direction velocity changes.

3. Sometimes, acceleration is a constant
Example: Acceleration due to gravity is constant near the surface of the Earth.
Since it is a constant, the acceleration due to gravity is given the special symbol g.
For the earth, g = 9.8 m/s/s or approximately 10 m/s/s.

4. When Acceleration = g, we have Free Fall Motion.
Notice that the V arrow gets longer while the g arrow does not. It remains constant in length and direction.
V = 0m/s
t = 0 seconds g
V(t) = V(0) + g(t)
V(2sec) = 0 + (10m/s2)(2s)
V(2sec) = 20m/s
V = ?
t = 2 seconds g

5. Gravitational Acceleration Near the Surface of the Earth.
On the Earth, the acceleration due to gravity is ~ 10m/s2 (9.8 m/s2).

6. Momentum and Force V p – linear momentum m p = mV
Momentum = Mass x velocity
Force = (Change in Momentum)/(Change in time). V
p – linear momentum m
p = mV
Example: If m = 10kg and V = 10m/s (East)
P = (10kg)(10m/s) = 100 kg m/s (East)

7. Conservation of Linear Momentum and Conservation of Angular Momentum
In the absence of a net external force, linear momentum remains constant.
Conservation of Angular Momentum:
In the absence of a net torque (twisting force), the total angular momentum of a system remains constant.

10. Mass and Weight Mass : Amount of matter a body possesses.
Weight : Force of gravity acting on the mass.
Apparent weight = Net force that acts on the mass.

11. Weight is not the same as mass
Weight is not the same as mass. The man’s weight changes, but his mass remains constant.

12. Free-fall, Weightlessness, and Orbit
Free-Fall- the condition of an accelerating mass when the acceleration = g.
Weightless- If the only force acting is that due to gravity, and there is no reaction force from a floor, for example, pushing up against you, then one is in a state of free-fall and experiences weightlessness.

13. Astronauts are in a prolonged period of weightlessness when they are in orbit

15. Weightlessness

17. Newton’s Cannon
The faster the cannonball is shot, the farther it goes before hitting the ground.
If it goes fast enough, it will continually “fall around” or orbit, the Earth.
With a fast enough speed, it may escape the Earth’s gravity altogether.
Escape velocity – The minimum velocity needed to escape from the gravitational field of a moon, planet or star.

18. Newton’s Three Laws of Motion
1) Law of Inertia: In the absence of a net force, the motion of an object remains constant.
2) Net Force = Rate of change of momentum.
Momentum = mass x velocity (F = ma)
3) For every force, there is always an equal and opposite reaction force.

19. Matter and Energy in Everyday Life
Matter is simply material, such as rocks, water, or air.
Mass is the amount of matter an object has.
Energy:
In physics, energy is defined as the ability to do work.
Generally two types of energy:
1) Kinetic
2) Potential
We measure energy in calories, Joules, electron volts, along with many other units.

20. Whenever matter is moving, it has energy of motion, or kinetic energy.
Kinetic Energy = Energy of motion.
Potential Energy = Usually energy of position, but can also be regarded as stored energy.
Gasoline has stored chemical potential energy which is converted to kinetic energy of the car.
Radiative Energy = Energy of light (electromagnetic energy).

22. A Scientific View of Energym
We can calculate the kinetic energy of any moving object with a very simple formula:
KE = ½ mv2
m : Mass of the object v: Speed of the object KE: Kinetic energy measured in Joules.

23. Types of Potential Energy
Gravitational Potential Energy
The amount of gravitational potential energy released as an object falls depends on its mass, the strength of gravity, and the distance it falls.
GPE = mgh.
Mass-Energy E = mc2
A small amount of mass represents a huge amount of energy.

25. Thermal Energy
The energy contained within a substance as measured by its temperature is often called thermal energy.
Thermal energy represents the collective kinetic energy of the many individual particles moving within a substance.

27. Temperature and Heat
Lower Temperature
Higher Temperature

28. Same Temperature, but less thermal energy.
Same Temperature, and more thermal energy.

29. Phases/States of matter:
Phase Changes
Phases/States of matter:
Solid
Liquid
Gas
Plasma

30. Phases of Matter – example: water
Finally, at 100oC (STP), the water molecules have enough thermal energy to break free from one-another.
Evaporation begins with the production of steam (water vapor).
The water remains a liquid over a large temperature range.
As the temperature increases, the water becomes a liquid (liquid water)
Below 0oC (32oF), water is a solid (ice)
Ref: PJ Brucat (University of Florida)

32. Conservation of Energy
A fundamental principle in science is that, regardless of how we change the form of energy, the total quantity of energy never changes. This principle is called the:
Law of Conservation of Energy

33. Newton’s Law of Universal Gravitation
Every mass attracts every other mass through the force called gravity.
The force of attraction is directly proportional to the product of their masses.
The force of attraction decreases with the square of the distance between the mass centers. This is called an inverse square law.

34. The Gravitational Force Fg

35. The “Why” of Kepler’s Laws, and More
Newton found that Kepler’s first two laws apply not only to planets, but to any object going around another object under the force of gravity.
He found that orbits do not have to be bound orbits as they are with elliptical orbits Unbound (hyperbolic) orbits are also possible.
Newton found that Kepler’s third law could be generalized in a way that allows us to calculate the mass of one or both orbiting objects.

37. Tides
The tidal bulges face toward and away from the moon because of the difference in the strength of the gravitational attraction in parts of the Earth at different distances from the Moon.
There are two daily high tides at any location on Earth, as it rotates through the two tidal bulges.

39. Tides also depend on tidal forces from the Sun, which are about 1/3 as strong as the moon’s.
Highest high tides.
Lowest low tides.

40. Tidal Friction causes three important effects
It causes the Earth’s rotation to gradually slow down, resulting in a longer day.
It makes the Moon move gradually away from the Earth (The Moon has a slight tangential component to its acceleration vector)
Synchronous rotation is a natural consequence of tidal friction.

41. Tangential acceleration
Radial acceleration
It can be shown, by conservation of angular momentum, that the radial distance of the moon must increase as the rotation rate of the Earth decreases by tidal friction.

42. Pluto-Charon system – another example of synchronous rotation

43. Orbital Energy and Escape Velocity
A comet in an unbound orbit of the Sun, passes near Jupiter.
The comet loses some of its orbital energy to Jupiter, which changes the comet’s path to a bound orbit around the Sun.
unbound orbit
bound orbit

44. The escape velocity of the Earth = 11 km/s
The escape velocity is the velocity necessary for an object to completely escape the gravity of a large body such as a moon, planet or star.
The escape velocity of the Earth = 11 km/s
G = 6.67 x m3/kg s2
M = Mass of the planet
R = Radius of the planet

45. Newton’s 3rd law of motion states:
In the absence of a net force, the motion of an object remains constant.
For every action there is always opposed an equal reaction.
F = ma

46. Newton’s Law of Universal Gravitation states:
The gravitational force is proportional to the distance between masses.
The gravitational force is inversely proportional to the distance between masses.
The gravitational force is proportional to the square of the distance between masses.
The gravitational force in inversely proportional to the square of the distance between masses.

47. End Section