7. Universal Motions
Reading: Chapter 6
I derive from the celestial phenomena the forces of gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions which are also mathematical, I deduce the motions of the planets, the comets, the moon and the sea.
Before Newton, the laws of heaven and Earth were separate--celestial
objects were thought to "naturally" go in circles while earthly
objects were known to "naturally" fall straight down when dropped.
Newton derived general laws of physics from looking at celestial objects.
We will do things the other way around, first looking at these laws of
and then applying them to celestial objects.
|(1) What is the difference between a law and a theory? (Between an axiom and a hypothesis?)|
We will be thinking about motion some more - let's remind ourselves about distance, speed, acceleration, etc.;
Stationary = stopped = nothing changing with time
Speed = moving = change in distance with time
But what about direction? It helps to know in what direction you are headed. Here we can introduce velocity which is used to include both direction and speed.
This modifies our way of thinking of acceleration:
Acceleration = change in velocity
= change in speed or direction or both
(2) How many different controls are there in a car for causing it to accelerate? Name each and give a brief explanation of each. (Hint: there are 3, at least)
(3) Look back at Galileo's Law of Inertia What was this inertia stuff? Which has more inertia, a brick or a feather? A ton of bricks or a ton of feathers?
An object at rest tends to stay
at rest. An
object in motion tends to continue in motion at constant speed in
(He also said: "If I have seen far, it is because I have stood on the shoulders of giants," meaning Galileo of course...)
|Newton's First Law of Motion: |
Every body continues in a state of rest or in a state of uniform motion in a straight line unless it is compelled to change that state by a force acting on it.
The property of objects that makes them "tend" to obey Newton's 1st law is inertia. Inertia is the resistance to changes in motion. You have probably gathered by now that the amount of inertia a body has is measured by its mass. Massive objects have lots of inertia, meaning that a large force is required to change their motion.
|(4) To ride quickly around an obstacle
course you want to ride a
vehicle that is which of the following? |
(a) heavy and able to squash the obstacles
(b) light and maneuverable
(c) brightly colored to attract attention
When you are in a car that strongly accelerates--say, the driver stomps on the accelerator or turns the wheel sharply --you feel a FORCE. These are the forces that the car has to exert on you to overcome your inertia and accelerate YOU--otherwise you would be left behind or not get around the bend with the car.
Newton put this relationship among FORCE, MASS and ACCELERATION into mathematical form with Newton's Second Law:
|Newton's Second Law of Motion:
When a force F acts on a body of mass m, it produces in it an acceleration a equal to the force divided by the mass.
Another, perhaps simpler, way of saying the same thing is:
|A body accelerates when an unbalanced force is applied--the greater the force, the greater the acceleration--the smaller the body's mass, the easier it is to be accelerated.|
Or, yet other way is:
|The more force on an object, the more it accelerates. But the more massive it is, the more it resists acceleration.|
|(5) In the following diagrams there are plenty of FORCES--yet nothing is moving--why not?|
(6) The original Honda Civic car was a metal shell (plus seats, stereo, etc.;) around the same engine as the Honda 1000cc motor bike. The car and bike engines could deliver the same FORCE, but the car had all that extra MASS. Use Newton's Second Law to show which will have the greater ACCELERATION--the car or the bike?
(7) Pitchers can throw baseballs so that they reach 90 MPH when they reach the batsman. That means the pitcher applies a force that accelerates the ball from 0 to 90 MPH in fractions of a second. Impressive. If baseballs were made of iron or stone instead of rubber and leather (or whatever they are made of) so that the balls were twice their normal mass, how much greater force would the pitcher have to apply to achieve the same acceleration?
Finally, we come to
|Newton's Third Law of Motion: |
To every action there is an equal and opposite reaction.
This law is sometimes called the law of action and reaction. There is never a single isolated force in nature. If you look closely, there is always an oppositely-directed counterpart. This is easiest to see when the forces involved are applied through collisions--e.g. in snooker or billiards.
|Before: cue ball moves with velocity V, 8-ball is stationary||Collision: Cue ball exerts force F on 8-ball. 8-ball exerts equal but opposite force on cue ball.||After: 8-ball moves with velocity V. Cue ball is stationary.|
The forces that the balls exert on each other have the same strength but opposite directions. Because the balls have the same mass, their accelerations and the resulting changes in speed and direction have the same magnitude.
|(8) In each of frames A, B and C, how many forces are acting?|
When a truck and a bicycle collide each feels a force of the same magnitude during the collision. But the resulting accelerations will be different.
(9) As a result of the collision between the truck and the bicycle,
(a) the change in the bike's velocity is big / little / none
(b) The change in the truck's velocity is: big / little / none
The law of action and reaction is the basis of rocket propulsion:
(10) Are Laws of Physics the same as Federal Laws -- does the exact wording matter?
(11) Why can't airplanes fly in space? Why do we need rockets?
|The rocket exerts a downward push on the exhaust gases. The gases push back, by Newton's Third Law. If this upward thrust exceeds the weight of the vehicle, up we go!|
We are gearing up to get into space - but first let's make quite sure we've gotten Newton's Laws of Motion down by doing a few more exercises:
(12) Imagine you are swinging a ball on a string in a circle above your head, with the ball taking 2 seconds to complete a circle.
Try it! Tie a lump of something (a T-shirt? A paperback book? A plastic cup?) onto a piece of string--preferably in a wide open space where you cannot damage much.
(13) Earth orbits the Sun at a constant speed of 30 km/sec.
(14) If the Earth and Moon are feeling the same amount of force, why does the Moon orbit the Earth rather than the Earth orbit the Moon?
|Action = Reaction:
When I push on a wall, the wall pushes back with equal force. Similarly, FMOON = FEARTH
Newton united the objects of the heavens with earthly objects by showing that they all experience the same laws of motion. The key was to understand the force of gravity. So, let's get to the BIG stuff of GRAVITY...