Intro to Dynamics

We all have an intuition about how objects move. Our beliefs are hard to change since they work well in our day to day lives. But they limit us in developing an understanding of how the world works - we must build on our intuition and move beyond it. Intuitive Physics

Galileo vs. Aristotle In our experience, objects must be pushed in order to keep moving. So a force would be needed to have a constant velocity. This is what Aristotle claimed in his in his series of books entitled "Physics", written 2400 years ago. But 400 years ago, another scientist and astronomer, Galileo, proposed the following thought experiment which revealed another perspective.

Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen? Thought Experiment

Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

Thought Experiment Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

Thought Experiment Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

If a ball rolls down one ramp, it keeps rolling up the other side until it reaches the same height. Thought Experiment

Now repeat that experiment, but make the second ramp less steep. What Will Happen? Thought Experiment

Now repeat that experiment, but make the second ramp less steep. What Will Happen?

Thought Experiment Now repeat that experiment, but make the second ramp less steep. What Will Happen?

Thought Experiment Now repeat that experiment, but make the second ramp less steep. What Will Happen?

It will still keep rolling until it reaches the same height, but it has to roll farther! Thought Experiment

Finally, make the ramp flat. Now what will happen?

Thought Experiment Finally, make the ramp flat. Now what will happen?

Thought Experiment Finally, make the ramp flat. Now what will happen?

Thought Experiment Finally, make the ramp flat. Now what will happen?

Thought Experiment Finally, make the ramp flat. Now what will happen?

Thought Experiment Finally, make the ramp flat. Now what will happen?

Thought Experiment It will keep rolling forever, no external force is necessary.

Galileo vs. Aristotle It's not that Aristotle was wrong. In everyday life, objects do need to keep being pushed in order to keep moving. Push a book across the table. When you stop pushing, it stops moving. Aristotle is right in terms of what we see around us every day.

Force and Motion It's just that Galileo, and later Newton, imagined a world where friction could be eliminated. F applied F friction In the absence of all external forces, an object's velocity remains constant. Two equal and opposite forces have the same effect, they cancel to create zero net force. Friction represents an external force acting on the object, just as your push is an external force.

Newton's 1st Law of Motion

Sir Isaac Newton Galileo's observations were more fully formed in 1687 by the 'father of physics, ' Sir Isaac Newton, who called this observation "The First Law of Motion".

I. Newton's First Law of Motion In other words, an object maintains its velocity (both speed and direction) unless acted upon by a nonzero net force or an unbalanced fore. Having zero velocity, being at rest, is not special, it is just one possible velocity…a velocity which is no more special than any other. A n object at rest remains at rest, and an object in motion remains in motion, unless acted on by a net external force.

Newton's First Law of Motion Mass as a Measure of the Amount of Inertia All objects resist changes in their state of motion. The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion. A. Mass and Inertia

Force is a vector quantity-a push or a pull 1. Balanced forces: equal and opposite forces Balanced forces give no motion No motion of hands Newton's First Law of Motion B. Combining Forces

2. Unbalanced force – more force in one direction (net force)

Bigger force to the right Smaller force to the left Net force to the right

A.K.A. The Law of Inertia This law is often referred to as the "Law of Inertia." The word inertia comes from the latin word iners which means idle, or lazy. Inertia is the tendency of an object to resist any change in motion. Demo: hard boiled egg vs. raw egg. Click here.Click

1 In the absence of an external force, a moving object will Astop immediately. Bslow down and eventually come to a stop. Cgo faster and faster. Dmove with constant velocity. c c c c

2 When the rocket engines on a spacecraft are suddenly turned off while traveling in empty space, the starship will Astop immediately. Bslowly slow down, and then stop. Cgo faster and faster. Dmove with constant velocity. c c c c

3 A rocket moves through empty space in a straight line with constant speed. It is far from the gravitational effect of any star or planet. Under these conditions, the force that must be applied to the rocket in order to sustain its motion is Aequal to its weight. Bequal to its mass. Cdependent on how fast it is moving. D zero. c c c c

4 You are standing in a moving bus, facing forward, and you suddenly fall forward. You can infer from this that the bus’s Avelocity decreased. Bvelocity increased. Cspeed remained the same, but it's turning to the right. Dspeed remained the same, but it's turning to the left. c c c c

5 You are standing in a moving bus, facing forward, and you suddenly fall forward as the bus comes to an immediate stop. What force caused you to fall forward? Agravity Bnormal force due to your contact with the floor of the bus Cforce due to friction between you and the floor of the bus DThere is not a force leading to your fall. c c c c

Newton's laws are only valid in inertial reference frames: An inertial reference frame is one which is not accelerating or rotating. It is an area in which every body remains in a state of rest unless acted on by an external unbalanced force. Inertial Reference Frames

This is why a drink on the dashboard of a car can suddenly seem to accelerate backwards without any force acting on it. It's not accelerating, it's standing still. The reference frame, the car, is accelerating underneath it. Inertial Reference Frames When your car accelerates, it is not an inertial reference frame. Click here for a very famous video about frames of reference. watch the first 2:30 of the video

II. Nature of Force

A.Definition: A force is a push or pull resulting from the interaction between objects. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction stops, the two objects no longer experience the force. Forces only exist as a result of an interaction.

II. Nature of Force B.Type of Forces A force is a push or pull acting upon an object as a result of its interaction with another object. There are two broad categories of forces based on whether the force resulted from the contact or non-contact of the two interacting objects. Contact ForcesNon Contact Normal ForceGravitational Force Frictional ForceMagnetic Force TensionElectrical Force Air Resistance Force Applied Force Spring Force

There are many different types of forces that occur in nature, but perhaps none is more familiar to us than the force of friction (F fr ). 1. Friction - A Resistive Force Friction is a resistive force that opposes the motion of an object. What does sandpaper have to do with friction?

Friction is the reason objects stop rolling or sliding along a surface. It is the reason it is difficult to start pushing a heavy box along the floor. Friction - A Resistive Force There are many different types of friction: Friction between solid objects and air is often called air resistance. Friction between two fluids is called viscosity, and so on.

a. Factors affecting friction: Friction - A Resistive Force Type of surfaces How hard surfaces are pressed together

b. Static v. Dynamic Friction Static Friction that acts on something that is not moving; No heat or wear is generated Dynamic Friction, aka Kinetic Friction, results from contact between moving objects (sliding, rolling, fluid)

2. Gravity – force of attraction between two objects -- pulling force a. Factors Affecting Gravity i. Mass – more mass, more gravity ii. Distance – closer, more gravity

b. Weight vs. Mass Define: weight: force of gravity on an object (F w ); dependent on location of the object (due to masses and distances) mass: amount of matter an object contains; does not change with location 1 kilogram mass has a weight of 9.8 N (on earth)

3. ‘Other’ In this unit, we will be concerned with weight (force of gravity on an object) and friction (force that opposes motion). We will also conside other contact forces: Normal Force Applied Force Tension Air Resistance