Download Class 11 - Rice University

ASTRONOMY 202 Spring 2007: Solar System Exploration
Instructor: Dr. David Alexander
Web-site: www.ruf.rice.edu/~dalex/ASTR202_S07
Class 11: Newton’s Laws [2/9/07]
Announcements
Gravitational acceleration
Mass, weight and fun on elevators
One good apple
• Newton’s 3 Laws of Motion
• Conservation of Momentum
• Conservation of Angular Momentum
Chapter 4
Newtonian Gravitation
• Universal Law of Gravitation
• ‘Falling’ Orbits
• Generalizing Kepler’s Laws
• Tricking gravity
Tidal Forces and Orbital Energy
Announcements
Homework 4 available online – due Mon Feb 12
Guidelines for Discussion papers online
• Discussion paper due Mon Feb 19
Observing night planned for sometime next week, weather permitting
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.
On the surface of the Earth: P = mgh
Mass-Energy
E = mc2
The energy
produced in the
center of stars is
generated entirely
from matter.
Conservation of Energy
We can change the form of energy from one to another but
the total quantity of energy never changes.
This is called the law of conservation of energy and is one of the
cornerstones of science.
Gravitational Acceleration
Acceleration due to gravity: g = 9.81 m/s2
This value holds at the surface of the Earth.
a15_ham_feather1.mov
Momentum and Force
Momentum – the product of an objects mass and velocity: p = mv
Force – the thing that causes a change of momentum: F = ma
- strictly speaking this should be net force
Mass and Weight
Mass on Earth = 100 kg
Weight at surface of Earth = 100 kg
Mass on Moon = 100 kg
Weight at surface of Moon = 16 kg
Newton’s Laws of Motion
If I have seen further it is by standing on the shoulders of
giants.
Letter to Robert Hooke, February 5, 1675
Philosophiae Naturalis Principia Mathematica (1687),
Sir Isaac Newton (1642-1727)
Newton invented calculus several years prior to
Leibniz but did not publish his results.
Newton modified the
conventional telescope
to provide an off-axis
focus.
2.5 m Isaac Newton Telescope
La Palma, Canary Islands
Newton’s First Law
I. In the absence of a net (overall) force acting upon it an object
moves with constant velocity
Thus, objects at rest will tend to stay at rest while an object in motion stays in
motion with no change in velocity. This is called an object’s inertia.
Newton’s Second Law
II. The acceleration of an object as produced by a net force is
directly proportional to the magnitude of the net force, in the same
direction as the net force, and inversely proportional to the mass of
the object.
Units?
Force = rate of change of momentum
or
Force = mass x acceleration (F=ma)
Thus, objects of different mass will accelerate differently when subjected to
the same force.
Also applies to angular motion
Inward force implies inward acceleration
Newton’s Third Law
III. For any force, there is an equal and opposite reaction force
or
For every action there is an equal and opposite reaction
Thus, forces always come in equal and opposite pairs.