Today’s Lectures: The Laws of Gravity Speed, velocity, acceleration, force Mass, momentum and inertia Newton’s three laws of motion The Force of Gravity

Assigned Reading Chapter 5.1

Before Newton Kepler understood the phenomenology of planetary motions, I.e. the three laws, but never understood *why* planets move the way they do –He thought of magnetic force from the Sun –He even thought (and dismissed) that Angels pull planets along their orbits Galileo understood inertia, force and acceleration very well, but fell short of understand the causal relationship between force and acceleration. He also did not propose a universal law for the force of gravity

Describing Motion Motion is when the position of an object changes in time If position does not change, the object is at rest The describe motions we need to monitor position and time The rate at which an objects covers a given amount of space in a given amount of time is called speed – v = s/t

Vectors, or things with a sense of direction There are physical quantities in nature for which only one number, their intensity, tells the whole story: e.g. temperature, mass, luminosity, color Other quantities need both an intensity and a direction to be fully described: e.g. speed, force, acceleration. These quantities with a “direction” are called VECTORS

Galileo and the Concept of Inertia Aristotle held that objects at rest remained at rest unless a force acted on them, but that objects in motion did not remain in motion unless a force acted constantly on them: F = v WRONG. Galileo concluded that an object in a state of motion possesses an ``inertia'' that causes it to remain in that state of motion unless an external force acts on it RIGHT.

Galileo’s Law of Inertia But velocity cannot not the whole story: we need a more general concept to describe motions: momentum P = m·v An object maintains its “quantity of motion” (momentum), unless a force is acted upon it Only a force can change the “quantity of motion” (momentum) of an object, either by changing its speed, or by changing its direction of motion, or both

More on Momentum Momentum is a quantitative way to describe an object’s tendency to continue to do whatever it was previously doing. An object’s momentum is simply its mass times its velocity. P = m·v Don’t forget that velocity is a vector, so momentum is a vector: the direction of motion is very important!

Should a heavy object fall faster than a light one, as Aristotle believed?

Sir Isaac Newton and the Unification of Physics & Astronomy Newton was by many standards the most important figure in the development of modern science. He demonstrated that the laws that govern the heavens are the same laws that govern the motion on the surface of the Earth. Newton's Three Laws of Motion. Theory of Universal Gravitation ( )

Newton’s First Law (really, Galielo’s Inertia Law) In the absence of a net force, an object moves with constant velocity, or it conserves its momentum. (paraphrased) If nothing acts on an object, the object will keep moving in a straight line and at a constant speed. The same is true for zero velocity.

There must be a force acting on the apple. What force? More importantly, if the force of gravity reaches to the tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon!

Vocabulary Words Speed is the distance traveled in each second – it’s measured in meters per second (m/s). Velocity is the speed in a particular direction – it’s measured in meters per second (m/s). Acceleration is the change in velocity in each second – it’s measured in meters per second per second (or m/s 2 )

Acceleration An acceleration is a change in velocity. Acceleration occurs when either the magnitude or direction of the velocity (or both) are altered. Uniform Circular Motion is Accelerated Motion How many ways can your car be accelerated?

Which of the following does NOT describe an acceleration: a car traveling with constant speed around a bend a car decreasing speed on a straight road a car traveling with constant speed on a straight road a planet traveling around a Sun

Newton’s First Law can also be stated as: In the absence of a net force, the acceleration of an object must be zero If an object is being accelerated, there must be a net force exerting on it

Newton’s Second Law Acceleration is caused by force but also related to the mass of the object Force = Mass x Acceleration F = m·a Or a = F/m

Survey Question Two identical spacecraft are to be accelerated by rockets. The first rocket fires with a force 4 times as great as that of the second rocket. The acceleration of the first rocket is _____ times as great as the acceleration of the second rocket. 1) 1/4 2) 1/2 3) the same 4) 2 times 5) 4 times

Question: How do objects accelerate due to the force of gravity? The gravitational force on an object near the surface of Earth is: F grav = m·g (g = 9.8m/s 2 )

Newton’s Third Law For every ACTION (I.e. application of a force) there is an equal and opposite re- ACTION F 1 = -F 2

Newton’s Third Law For any force, there always is an equal and opposite reaction force. Table pushes back on box Box pushes down on table due to gravity.

The Third Law demonstrated: without external force, momentum is conserved If one object at rest (I.e. v=0) is suddenly separated into two parts, one moves in one direction and the other must move in the opposite direction! After separation: P 1 = m 1 ·v 1 P 2 = m 2 ·v 2 P 1 + P 2 = m 1 ·v 1 + m 2 ·v 2 = 0 THUS: m 1 ·v 1 = -m 2 ·v 2 THUS: To the force that created the first motion… there is an opposite-acting force that creates the second motion

Example: The Jet Engine What makes a jet-propelled airplane move forward?

Gravity What force is responsible for motions in the universe? What force makes objects fall? What keeps us on the rotating Earth? Why don’t planets move in straight lines, but orbit around the Sun instead?

Gravity We can summarize the universal law of gravitation with the following statements: –Every mass attracts every other mass through the force of gravity. –If mass #1 exerts force on mass #2, and mass#2 exxerts force on mass#1, the force must depend o both masses, namely: –The force of attraction is directly proportional to the product of the two masses. –The force of attraction is inversely proportional to the square of the distance between the masses.

The Law of Gravity d M1M1 M2M2 G = 6.67x m 3 /kg/s 2 Near Earth’s surface

Mass and Weight Mass is a measure of how much material is in an object. Weight is the force exterted by gravity on a massive body (body with mass), e.g. placed on the surface of Earth Weight is a measure of the gravitational force exerted on that material. Thus, mass is constant for an object, but weight depends on the location of the object. Your mass is the same on the moon, but your weight on the surface of the moon is smaller

Survey Question Two equal masses, m, separated by a distance, d, exert a force, F, on each other due to their gravitational attraction. How large is the gravitational force between an object of mass m and an object of mass 2m separated by the same distance d? ¼ F ½ F F 2F 4F

Survey Question Two equal masses, m, separated by a distance, d, exert a force, F, on each other due to their gravitational attraction. How large would their gravitational attraction be if the distance between them was doubled? 1) ¼ F 2) ½ F 3) F 4) 2F 5) 4F

Survey Question If aliens magically turned our Sun into a black hole of the same mass but 10 times smaller in diameter, what would change about the Earth’s orbit? 1) it would be 10 times smaller in radius 2) it would spiral into the black hole 3) nothing would change 4) it would spiral away from the black hole 5) it would be 10 times larger in radius

… so why don’t planets just fall into the sun? M1M1 M2M2

… because they miss (that is, they have enough tangential velocity to always miss) M1M1 M2M2 v This is the concept of an orbit. FgFg FgFg

Why doesn't the earth fall to the sun? It has a velocity and it has inertia! Force of gravity causes change in the direction of velocity --- acceleration. The earth is falling towards the sun all the time!

V=8km/s

Why don't they fall? They are circuling Earth at a speed of 8 km/s!

Quiz  Astronauts inside the space shuttle float around because ____ they are falling in the same way as the space shuttle.  If you are in a free-falling elevator, you are massless. (true or false) false