Newtons Laws of Motion Background Sir Isaac Newton

Newton’s Laws of Motion

Background Sir Isaac Newton (1643 -1727) an English scientist and mathematician famous for his discovery of the law of gravity also discovered the three laws of motion. He published them in his book Philosophiae Naturalis Principia Mathematica (mathematic principles of natural philosophy) in 1687. Today these laws are known as Newton’s Laws of Motion and describe the motion of all objects on the scale we experience in our everyday lives.

“If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent. ” -Sir Isaac Newton

Newton’s Laws of Motion 1. An object in motion tends to stay in motion and an object at rest tends to stay at rest unless acted upon by an unbalanced force. 2. Force equals mass times acceleration (F = ma). 3. For every action there is an equal and opposite reaction.

Newton’s First Law An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by an unbalanced force.

What does this mean? Basically, an object will “keep doing what it was doing” unless acted on by an unbalanced force. If the object was sitting still, it will remain stationary. If it was moving at a constant velocity, it will keep moving. It takes force to change the motion of an object.

What is meant by unbalanced force? If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes.

Some Examples from Real Life A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion. Two teams are playing tug of war. They are both exerting equal force on the rope in opposite directions. This balanced force results in no change of motion.

Newton’s First Law is also called the Law of Inertia: the tendency of an object to resist changes in its state of motion The First Law states that all objects have inertia. The more mass an object has, the more inertia it has (and the harder it is to change its motion).

More Examples from Real Life A powerful locomotive begins to pull a long line of boxcars that were sitting at rest. Since the boxcars are so massive, they have a great deal of inertia and it takes a large force to change their motion. Once they are moving, it takes a large force to stop them. On your way to school, a bug flies into your windshield. Since the bug is so small, it has very little inertia and exerts a very small force on your car (so small that you don’t even feel it).

If objects in motion tend to stay in motion, why don’t moving objects keep moving forever? Things don’t keep moving forever because there’s almost always an unbalanced force acting upon it. A book sliding across a table slows down and stops because of the force of friction. If you throw a ball upwards it will eventually slow down and fall because of the force of gravity.

In outer space, away from gravity and any sources of friction, a rocket ship launched with a certain velocity and direction would keep going in that same direction and at that same velocity forever.

Newton’s Second Law Force equals mass times acceleration. F = ma Acceleration: a measurement of how quickly an object is changing velocity.

What does F = ma mean? Force is directly proportional to mass and acceleration. Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force. Now imagine we make the ball twice as big (double the mass) but keep the acceleration constant. F = ma says that this new ball has twice the force of the old ball. Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again have twice the force of the ball at the original acceleration.

More about F = ma If you double the mass, you double the force. If you double the acceleration, you double the force. What if you double the mass and the acceleration? (2 m)(2 a) = 4 F Doubling the mass and the acceleration quadruples the force. So. . . what if you decrease the mass by half? How much force would the object have now?

What does F = ma say? F = ma basically means that the force of an object comes from its mass and its acceleration. Something very massive (high mass) that’s changing speed very slowly (low acceleration), like a glacier, can still have great force. Something very small (low mass) that’s changing velocity very quickly (high acceleration), like a bullet, can still have a great force. Something very small changing velocity very slowly will have a very weak force.

The Law of Gravitation Falls within Newton’s 2 nd Law

Gravitation • Every object with mass attracts every other object with mass. – Newton realized that the force of attraction between two massive objects: • Increases as the mass of the objects increases. • Decreases as the distance between the objects increases.

Gravitational Field • Gravitational field – an area of influence surrounding a massive body. – Field strength = acceleration due to gravity (g). • So gravity causes mass to have weight.

Weight vs. Mass • Mass is how much stuff makes up you. • Weight is the force of gravity of your mass. • When you stand on a scale you are truly finding your mass. Your mass and weight are only the same here on Earth (even then your weight can change based on gravitational fluxes)

Losing weight • To lose weight you must decrease gravitational force (go to the moon!) • To increase weight you must increase gravitational force (go to Jupiter!)

Gravitational acceleration • Yesterday you saw that gravity has a set acceleration depending on the mass of an object. • What is it here on earth? – Newton’s second law f=ma – With gravity (Earth) f= m x 9. 8 m/s 2

Variations in Gravitational Field Strength

Things Newton Didn’t Know • Newton didn’t know what caused gravity, although he knew that all objects with mass have gravity and respond to gravity. • To Newton, gravity was simply a property of objects with mass. • Newton also couldn’t explain how gravity was able to span between objects that weren’t touching. – He didn’t like the idea of “action-at-a-distance”.

Law of Universal Gravitation • FG = G M 1 M 2 r 2 • G = Gravitational Constant – G = 6. 67 x 10 -11 N*m 2/kg 2 • M 1 and M 2 = the mass of two bodies • r = the distance between them

Discovery of Neptune • Newton’s Law of Universal Gravitation did a very good job of predicting the orbits of planets. – In fact, the Lo. UG was used to predict the existence of Neptune. – The planet Uranus was not moving as expected. – The gravity of the known planets wasn’t sufficient to explain the disturbance. – Urbain Le. Verrier (and others) predicted the existence of an eighth planet and worked out the details of its orbit. – Neptune was discovered on September 23, 1846 by Johann Gottfried Galle, only 1º away from where Le. Verrier predicted it would be.

Other Things Newton Didn’t Know • Newton didn’t know that gravity bends light. – This was verified by the solar eclipse experiment you read about earlier this year. • He also didn’t know that gravity slows down time. – Clocks near the surface of Earth run slightly slower than clocks higher up. – This effect must be accounted for by GPS satellites, which rely on accurate time measurements to calculate your position.

Einstein and Relativity • Einstein’s theory of relativity explains many of the things that Newtonian mechanics cannot explain. – According to Einstein, massive bodies cause a curvature in space-time. • Objects moving through this curvature move in locally straight paths through curved space-time. – To any observer inside this curved spacetime, the object’s motion would appear to be curved by gravity.

Curvature of Space-Time

Curvature of Space-Time

Gravity: Not So Simple Anymore • According to Einstein, gravity isn’t technically a force. – It’s an effect caused by the curvature of space-time by massive bodies. • Why treat it as a force if it isn’t one? – Because in normal situations, Newton’s Lo. UG provides an excellent approximation of the behavior of massive bodies. – And besides, using the Lo. UG is a lot simpler than using theory of relativity, and provides results that are almost as good in most cases. – So there.

Newton’s Third Law For every action there is an equal and opposite reaction.

What does this mean? For every force acting on an object, there is an equal force acting in the opposite direction. Right now, gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force. This is why you are not moving. There is a balanced force acting on you– gravity pulling down, your seat pushing up.

Think about it. . . What happens if you are standing on a skateboard or a slippery floor and push against a wall? You slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed back on you with equal and opposite force. Why does it hurt so much when you stub your toe? When your toe exerts a force on a rock, the rock exerts an equal force back on your toe. The harder you hit your toe against it, the more force the rock exerts back on your toe (and the more your toe hurts).

Review Newton’s First Law: Objects in motion tend to stay in motion and objects at rest tend to stay at rest unless acted upon by an unbalanced force. Newton’s Second Law: Force equals mass times acceleration (F = ma). Newton’s Third Law: For every action there is an equal and opposite reaction.

Vocabulary Inertia: the tendency of an object to resist changes in its state of motion Acceleration: • a change in velocity • a measurement of how quickly an object is changing speed, direction or both Velocity: The rate of change of a position along a straight line with respect to time Force: strength or energy