Mechanics – the study of Motion Chapters 2 & 3 Mechanics – the study of Motion Herriman High Physics

What is Mechanics The study of how and why objects move is called Mechanics. Mechanics is customarily divided into 2 parts kinematics and dynamics. We will begin with the simplest part of kinematics – motion in a straight line. This is known as linear or translational motion. We will begin by discussing Newton’s First Law of Motion. Herriman High Physics

Frame of Reference In physics, Motion is relative. This means that in order to describe motion, you have to pick a “frame of reference” Frame of reference is always decided by the observer In physics we often use a coordinate axis to denote our frame of reference. Herriman High Physics

Frame of Reference Y -x x This is a familiar coordinate axis, but in physics it has a slightly different meaning. -Y Herriman High Physics

Frame of Reference In this frame of reference, up is positive, right is positive Down is negative, as is left Hence in physics a negative has no value, it merely denotes direction This is necessary because direction has a special distinction in physics; it separates vector quantities from scalar quantities Herriman High Physics

Chapter 2 Newton’s First Law Herriman High Physics

Newton’s First Law The Law of Inertia An object at rest tends to stay at rest. An object in motion tends to stay in motion. Herriman High Physics

Inertia: A resistance to change, a property of all matter. Herriman High Physics

Mass: A Measure of Inertia Mass is measured in kilograms Mass is not Weight Mass is a “built in” property of matter Just because you leave earth, you don’t change your mass, but you do change your weight Weight is a force caused by the acceleration due to gravity on the mass Herriman High Physics

Net Force and Equilibrium Net force is the sum of all the forces acting on an object When the net force on an object equals zero – the object is said to be in equilibrium. Herriman High Physics

Net Force and Equilibrium When a statue sits on the ground, the weight of the statue pushes downward and a support force* from the ground pushes upward, so the statue is in equilibrium * The support force is also called the Normal Force Fw FN Herriman High Physics

Sample Problem If a box with a weight of 20 Newton sits on a table, with what normal force does the table push back? A second, 10 Newton force is added to the top of the first box. Now what is the normal force exerted by the table on the 20 Newton box? What normal force is exerted by the 20 Newton box on the 10 Newton box? 20 N 10 N 20 N Herriman High Physics

Herriman High Physics

Herriman High Physics

Chapter 3 Linear Motion Herriman High Physics

Frame of Reference Earlier we said that in physics, Motion is relative. We talked about “frame of reference” and the fact that frame of reference is always decided by the observer So if you are standing still on the sidewalk and a car passes you at 60 m/s how fast is it going with respect to you? If that same car passes you at 60 m/s when you are riding in your car, traveling in the same direction at 30 m/s, how fast is it going with respect to you? Herriman High Physics

Vector vs. Scalar A Scalar Quantity is one that has only magnitude – distance is a scalar Example: If you travel 500 miles that is a distance A Vector Quantity is one that has magnitude and direction – displacement is a vector Example: If you travel 500 miles North this is displacement Herriman High Physics

Vector vs. Scalar If you divide distance by time you get average speed Example: S = D/t = 500 miles/2 hours =250 mph If you divide displacement by time you get average velocity Example: Vavg = x/t = 500 miles North/2 hours = 250 mph North Herriman High Physics

Acceleration Acceleration is defined as the change in velocity with respect to time a = Δv/t = (v2 – v1)/t Δ – the greek symbol delta represents change Example: If a car is traveling at 10 m/s and speeds up to 20 m/s in 2 seconds, acceleration is: a = (20 m/s – 10 m/s)/2 seconds = 5 m/s2 Herriman High Physics

Gravity & Free Fall Things fall because of the force of gravity. Gravity is an acceleration Near earth gravity has been experimentally calculated to be 9.8 m/s2 This means that the velocity of an object changes by almost 10 m/s each second. Herriman High Physics

Important Variables x – displacement – measured in meters v0 (Vnaught) – Initial Velocity – in m/s vf (Vfinal) – Final Velocity – in m/s a – acceleration – in m/s2 t – time – in seconds Herriman High Physics

Motion with Constant Acceleration Since a = (vf – v0)/t we can rearrange this to: vf = v0 + at and since x = vavgt and since vavg = (vf + v0)/2 A new equation is derrived: x = v0t + ½ at2 Herriman High Physics

Motion with Constant Acceleration Using this equation: x = v0t + ½ at2 and since we can rearrange a previous equation: vf = v0 + at to solve for time which gives us: t = (vf – v0)/a Substituting the second into the first we get: vf2 = v02 + 2ax Herriman High Physics

Summary of the Kinematic Equations Just a hint – Your “A” truly depends upon memorizing these and knowing how to use them! Vavg = x/t vavg = (vf + v0)/2 vf = v0 + at x = v0t + ½ at2 vf2 = v02 + 2ax Herriman High Physics

Recognizing Motion Graphs Graph A: No motion Graph B: Constant Velocity Graph C: Accelerated motion B Herriman High Physics