Today. Review. Momentum and Force Consider the rate of change of momentum. What is Momentum?

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1 Today Announcements: HW# is due Wednesday 8:00 am. HW#3 will be due Wednesday Feb.4 at 8:00am Review and Newton s 3rd Law Gravity, Planetary Orbits - Important lesson in how science works and how ultimately there are simple explanations for complex observations. All observations are unified under Newton s Universal Law of Gravity. Clicker questions Review Motion (position, velocity, acceleration) what causes acceleration? Force Force is a vector, it has a magnitude and a direction. A definition is given by Newton s Three Laws of Force If the net force on an object is zero the object will not accelerate. The amount of acceleration depends on the mass of the object and the amount of the applied force: F = ma. For every force, there is an equal and opposite force What is Momentum? Force is a push or a pull. A more precise and modern definition uses the concept of Momentum Momentum is mass times velocity Momentum is a vector. Often we write it as a p. Momentum and Force Consider the rate of change of momentum So another way of writing Newton s nd Law of Motion (F = ma) is: Modern analog of Galileo s notion of inertia

2 Typical Momentum HW Problem Typical Momentum HW Problem Motion in one dimension Positive force points in the +x direction Negative force points in the -x direction At what time is the net force equal to zero? Hint: Use the tangent line graphical technique for rates of change -5- What are the slopes of the tangent lines at the 3 indicated times? -6- Typical Momentum HW Problem Newton s 3rd Law: The Law of Force Pairs Gravity is pulling the book down; what holds it up? At t =.0 s the slope is positive => force is pointing in the +x direction At t = 1.40 s the slope is negative => force is pointing in the -x direction At t =.80 s the slope is zero => the net force is zero at this time -7- What s holding it up is a force exerted by the surface it s sitting on; this is called the normal force. The normal force is exactly equal and opposite to the gravitational force on the book -8-

3 Newton s 3rd Law: The Law of Force Pairs Forces always come in equal and opposite pairs. Remember that the forces are always equal in magnitude and opposite in direction! This simple law explains how rocket engines work -9- Newton s 3rd Law: The Law of Force Pairs Does this mean that the force exerted by the apple on the earth is equal and opposite to the force exerted on the earth by the apple? Indeed it does. Remember that the acceleration is inversely proportional to the mass Do you expect to notice the acceleration of the earth as an apple falls? No! -10- Walking and the Law of Force Pairs If you want to go next door, you walk. Watch your feet carefully as you take a step. You should be able to convince yourself that as you walk, you push backwards on the ground Therefore the ground is pushing forwards on you. This is the external force that accelerates you from rest (I.e., allows you to walk). Driving and the Law of Force Pairs What forces are exerted on a moving car?

4 Rockets and the Law of Force Pairs Intuition Alert: the Law of Inertia (Newton s 1st Law) Intuition : When nothing pushes on an object, that object slows There s nothing around to push backward in outer space; how are you going to move forward? to a stop. I.e., you must push it to keep it going. Think of a thrown ball that eventually comes to rest. The burning of the rocket fuel pushes the combustion products out the end; the combustion products push back. Physics : When nothing pushes on an object, that object coasts at constant velocity (I.e., doesn t speed up, slow down, or change direction). E.g., blow up a balloon and let it go Incidentally, the exhaust coming out your tailpipe does not have much effect on your car there s not enough mass coming out, and it s not moving fast -13enough. Intuition Alert: the Law of Force Pairs forces like air resistance, friction, or gravity. Once you eliminate these hidden forces, you will see that the law of inertia is correct Observing the Night Sky Intuition: If you push on an object and it pushes back on you with an equal and opposite force, these two forces would balance each other and nothing would ever accelerate. Therefore, the Law of Force Pairs cannot be right! Scientific process: a careful application of experience and reason to answer questions Example: Astronomy Resolution: The object indeed pushes you as hard as you push it, but these forces act on different objects and cannot balance each other. The object you are pushing experiences only your force on it and accelerates, as you know from your day-to-day experiences. Resolution: Objects such as a thrown ball experience hidden -15- Ancient peoples observed the night sky in great detail and took note of many regularities the behavior of stars and planets is not random. -16-

5 History of Observation of the Stars What you d see if you studied the night sky Detailed, recorded observations of the stars go back more than 5000 years. Many star names come from Babylonian and Chaldean times (4000 BC). 300 BC Aristarchus of Samos proposed a Sun centered solar system. This was rejected because it did not make sense that the Sun would be more important than the Earth. The stars do not move with respect to each other. Constellations stay the same There are a few (five) objects, visible to the naked eye, that appear starlike but do move across the fixed stars; these are the planets. The sun and moon also move across the stars The Celestial Sphere -18- Do stars move in circles around the earth? To us on Earth, it appears that all of the stars, Sun, Moon, and planets move on the underside of a large sphere. It would seem so from naïve observation The celestial sphere picture of the ancients doesn t seem too crazy! Time-elapsed photo of the night sky This sphere is called the Celestial Sphere. The ancients would have taken this picture literally

6 The Ancient Greek Earth-Centered Model The Ancient Greek Earth-Centered Model But the planets threw a monkey wrench into this perfectly spherical model; they do not move at a constant rate, and sometimes even move backwards (retrograde motion). universe is a series of concentric spherical shells, with the Earth at the center Each shell contained one object Sun, Moon, or planet and the stars were fixed to the outermost shell. -1- The Ancient Greek Earth-Centered Model -- Copernicus s Theory: A Sun-Centered Model Ptolemy attempted to accommodate this complex motion using epicycles smaller spheres around the planets. explained retrograde motion, but increasingly complex and clumsy model e.g., each planet has it s own set of epicycles (as many as 80) Click HERE or HERE for java applets of Ptolemy s model -3- Copernicus believed that the epicycles had become too complicated He looked for a much simpler solution, and came up with the Sun-centered model. Explains retrograde motion w/much simpler theory (Click HERE or HERE) -4-

7 Kepler s Improvements In the late 16 th century, Tycho Brahe made detailed observations of the motions of the planets, using the instrument shown. He found that the actual motions of the planets do not agree precisely with the predictions of the Copernican theory. -5- Johannes Kepler took Brahe s observations, and after years of calculation, concluded that the orbits of the planets are not circular they are ellipses, with the Sun at one focus. The orbits are only slightly elliptical, so the circular approximation was a good one. Kepler s Improvements -6- Kepler s Three Laws of Planetary Motion The Sun is at the center of the solar system with planets moving in ellipses around it. The planet moves faster when it is closer to the Sun. The square of the period (time for 1 orbit around the sun) is related to the cube of the semi-major axis of the orbit. The Dawn of the modern era of Science Roots of the scientific age: 1. Pythagorean belief in natural harmonies the universe is organized in a framework of principles that can be uncovered by observation. Copernican revolution the Earth is a planet similar to the other planets, and the natural world is fundamentally the same everywhere

8 Newton and the Universal Law of Gravity Story of the apple tree may or may not be true Gravity extends from the Earth to the moon! Newton s Universal Law of Gravity: Gm m F =! r 1 ; G = 6.673E 11 Nm Explains all observations of planetary motion, including Kepler s three laws, exactly. One equation unifies three laws! kg -9- Newton Explains Kepler s Laws Elliptical orbits Gm m F = 1 ; G = 6.673E! 11 Nm r kg The stronger force means more acceleration when the planet is closer to the star A larger distance means less force and a longer time for the orbit -30- Unification and Universality in Physics Prior to Newton, the motion of heavenly bodies (planets, stars, etc.) and the motion of earthly bodies (falling bodies, cannonball trajectories, etc.) were thought to be totally unrelated. Newton s 3 laws of motion + his theory of gravitation unified their description under 1 framework. We will see unification is a common theme in Physics. Newton s Universal Theory of Gravitation applies to ANY two objects with mass. Universality is another powerful theme we ll encounter repeatedly. -31-