In homework use full sentences.
Chapt 1 was about scientific methodology, measurement, about units, significant digits, unit conversions. Chapt 2 was about motion, speed, velocity and acceleration. Real motions that we observe and experience everyday are some combinations of constant speed, constant velocity, and acceleration. Last thing was projectile motion. Preview of chapt. 4: if something is accelerating it must have a NET force acting on it.
Topics in Chapter 4: Force: Newton’s laws of motion and law of gravity. Momentum: (a) momentum. (b) angular momentum and torque.
This is your first example of LAWS. Scientists look for LAW and ORDER in the universe. Recall from first class what a law is: a concise statement, in words or in a mathematical formula, about a fundamental relationship of nature.
Force and Net force.
WHAT is a force? Let’s not use the long sentence in the book. This is what I was taught and I haven’t found any reason why it shouldn’t be the definition of force. A FORCE IS A PUSH OR A PULL. Very common definition, but applies even to atoms, electrons, nuclei. Four types of force have been discovered, only four. Physicists have nearly unified them into one, but are having trouble putting gravity into the same theoretical framework as the supposedly unified three quantum field theory forces (electromagnetism, weak nuclear, strong nuclear).
Recall from previous chapter, most things aren’t moving out there—not visibly, anyway. There’s some swaying of the tree limbs in the breeze, but the trees stay put. Buildings and streets and signs also. The traffic signal hanging out over the street. Not moving. Are any forces acting on these things that are not moving? A building for instance? Yes, gravity is one. Gravity is trying to collapse all buildings to the ground. What else? The air! Air can produce very powerful forces.
Just because something isn’t moving doesn’t mean there aren’t any forces acting on it.
We’ve studied two kinds of motion: velocity and acceleration.
If something isn’t moving at all or is moving at a constant velocity then there is no NET force acting on it.
IF a NET force acts on a body, then the body accelerates. Another name: Net force = an unbalanced force.
When you push or pull on something, does that something move? Only if you use enough force.
When a push or pull occurs, it must be in some direction. VECtor! Force is a vector.
External vs. internal forces – later, discussing momentum.
NEWTON’s LAWS OF MOTION, and of Gravitation.
Aristotle thought and taught that an object in motion had to have a force acting on it—an earthly object. Their natural state, he said, was being at rest. Heavenly objects were different, and their natural state was being in perfectly divine eternal motion. Heaven and Earth, quite different realms. Until Copernicus, Kepler, Galileo, and, especially, Newton. Newton discovered universal gravitation. Heaven not so divinely different from earth! Uh-oh.
Newton’ 1st Law: Inertia. An object remains at rest or in uniform motion unless a net force acts on it.
Mass is a measure of amount of inertia.
2nd Law: Newton, building on Galileo’s ideas of inertia, mass, and acceleration, claimed that acceleration is proportional to something he (Newton) called force, and also that the acceleration produced by a constant force is inversely proportional to the mass being accelerated. These two relations can be expressed as
F=ma,
Or in words, Net force equals mass times acceleration.
“Net force” means the sum of the forces acting on the object. That’s shown in the example. Show it. Page 53.
If the net force is zero, the object remains at rest or moves with a constant velocity. When you use Newton ‘s 2nd law, you isolate on object and only talk about the forces on it, not the forces it exerts on other objects. Examples:
Sitting in your chair. The force of gravity is pulling down on you, the chair is pushing up. But see Newton’s third law, below, for explanation…
Driving at constant speed—are there forces acting horizontally on your car? Air resistance and friction in moving parts; and force of the tires pushing back on the roadway. The net force is zero when these forces balance. To unbalance the forces, push down on or let off of the accelerator. Acceleration will occur! (Yeh, you can call the slowing down deceleration.)
Weight : If you jump off the table, you accelerate according to F=mg, where m is the mass of your body and g is the acceleration due to gravity, I’ll come back to this after we do Newton’s 3rd law---
Newton’s 3rd Law: Forces always come in action/reaction pairs. The action force acts on one object and the reaction force acts on another object.
Example: What are all the action/reaction pairs for a person sitting in a chair? First, earth’s gravity acting on you; the reaction force is your body pulling back on the earth! What about the upward force the chair exerts on you? You exert a downward reaction force on the chair. Draw it.
Horse and cart: What constitutes an action/reaction pair? A pair of forces that act on a pair of objects, not on just one object. This is why action/reaction forces are equal and opposite but don’t cancel.
Law of Gravity: before Newton, gravity was just an English word having to do with heaviness or seriousness, the opposite of the word levity, meaning lightness or humor. Since the time Newton discovered universal gravitation, gravity also means
F= G m1m2/r2
which says two objects having masses m1 and m2 separated by a distance r attract each other with this force.
How does this reduce to F= mg? Show. What is the radius of the earth?
Momentum: Linear and Angular. Are important because of the conservation laws associated with them.
Linear: p=mv. Can calculate with this using the law of conservation of linear momentum:
If no external unbalanced forces act on it, the total linear momentum of an isolated system is constant. Ice skaters example.
Examples homework pfinal = pinitial
Angular momentum: First have to define torque: torque = lever arm times force. Lever arm is distance to the center of motion from where the force is acting. Wrench, figure 3-20. Angular momentum of an object is its mass times its velocity times the distance from it to the axis of rotation: L = mvr The “lever arm” distance is r.
Law of conservation of angular momentum: If no external unbalanced torque acts on an object the angular momentum of the object remains constant. Lfinal = Linitial Example of ice skater bringing in arms and increasing angular speed.
