Physics - Semester 1

Useful Links in the Understanding of General Physics

Chapter 1 - Introduction

Objectives

Basic Concepts

    Physics is one of the most basic of all the sciences.  It involves the structure and behavior of matter as well as the interactions between matter and the various forms of energy.  Some of the topics we will discuss are motion (mechanics), sound, and electricity.

    The quantitative description of behaviors of matter and energy is a fundamental part of the study of physics.  We will therefore start our semester with a quick review of the following mathematical concepts.

1. Scientific notation

2. Significant figures

3. Uncertainty in measurements

4. Solving simultaneous equations

5. Geometry of similar triangles and parallel lines

6. Basic trigonometry functions (sine, cosine, and tangent)

    Conversion of units is a common task when working in science especially in physics.  This is because many of the constant used in our calculations have been developed using known units of measurement.   Several standardized systems of measurement have been developed.  These include the MKS, CGS and British systems.  Most problems in physics are solved using one of these 3 systems.

Sample Problems

Convert 12.5 km to inches.

12.5 km  (1 mile / 1.609 km) (5280 ft / 1 mile) (12 in / 1 ft)  =  492000 in. (3 significant figures)

Notice that each ser of parenthesis is a conversion factor where the numerator and the denominator are equal to each other and arranges such that the previous unit will cancel out.

    Dimensional Analysis Tutorial               

Chapter 2 - Describing Motion: Kinematics in One Dimension      

Objectives

Basic Concepts 

    Kinematics is the description of how objects move.  It is not concerned with why they are put into motion.  We will attempt to describe the motion of various objects quantitatively by using a set of equations, which have been developed.  The terms we will use to talk about these motions are displacement (x), average velocity (v_avg), initial velocity (v_o), final velocity (v), and acceleration (a).

The relationships between these variables during uniformly accelerated motion are given in the following 5 equations:

• x = v_avg t

• v_avg = 1/2 (v_o + v)

• v = v_o + at

• v² = vo² + 2ax

• x = v_ot + 1/2 at²

    Objects moving horizontally or downward near the surface of the Earth will accelerate toward the ground at a constant acceleration g (9.80 m/s² or 32 ft/s²) if air resistance is ignored.  If projected upward the objects will decelerate at this same value.  

Sample Problems

1. Constant accelerated motion

2. Freely falling bodies

Chapter 3 -Kinematics in Two Dimensions: Vectors  

Objectives

Basic Concepts 

    Vectors, which are quantities with both magnitude and direction, can be added together to give a resultant vector, which will represent the net effect of the combination of all the vectors.  This will allow us to find the final motion of an object, which has several forces acting on it in several different directions.

    Components of vectors can be found using basic trigonometric functions.  A vector with a magnitude of v acting at an angle of f will be

            v_x = v cos f                    v_y = v sin f.

If the components of a vector are known, we can find both the direction and magnitude of the resultant vector by 

            v = (v_x2 + v_y2)^1/2            tan f = v_y/v_x

If air resistance is ignored, an object moving through the air near the Earth can be described through the use of vector addition.  Normally the horizontal component of its motion is considered to be constant whereas the vertical component will be under the influence of the gravitation acceleration of the Earth.  

Sample Problems

1. Vector addition

2. Projectile motion

Chapter 4 - Motion and Force:  Dynamics

Objectives

Basic Concepts 

        When studying the reasons for objects to begin, continue or stop moving in the real world we have begun to study dynamics.  Sir Isaac Newton developed 3 fundamental laws which govern how and why particles change their motion.   Listed below are his three laws of motion

1. Every body continues its state of rest or of uniform speed in a straight line unless acted on by a nonzero net force.  This tendency of a body to resist a change in motion is call Inertia.  The measure of inertia is called an object's mass.

2. The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass.  The direction of the acceleration is in the direction of the net force acting on the object.  This give rise to the equation SF = ma, which used to quantitatively describe the motion of any object.

3. Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.  This can be stated mathematically by F₁₂ = -F₂₁

        Weight is a term used to describe the gravitational force on an object.  It is proportional to the mass of the object and the acceleration of gravity at that point (W = mg).

        The primary focus of this chapter is force.  We will be studying how force effect objects, how they add together as vectors and how use these forces to predict the motion of an object.  The net force on an object is actually the vector sum of all the forces acting on that object.  The normal force (N) is the force a surface exerts on an object when it is placed that surface due to the object's weight.  The normal force is always directed perpendicularly to the surface.  Forces that retard the motion of an object are called frictional forces. Kinetic frictional forces and those that occur when an object is in motion and static frictional forces and when an object is at rest.  The equation for the computation of frictional forces is f = mN.

        When solving dynamics problems we will often turn to a free-bodied diagram for guidance.  A free-bodied diagram is a vector representation on a Cartesian coordinate system of the forces acting upon the object in question.  By using trigonometric functions we will be able to add common xy components together to fine net forces.  Newton's second law can then be applied to solve the problem.

Problem-Solving Strategy

Sample Problems

1. Free body diagrams and Newton's 2nd law

2. Dynamics 1

3. Inclined Plane

Chapter 5 - Circular  Motion:  Gravitation

Objectives

Basic Concepts 

        Uniform circular motion is defined as an object which traveling at a constant speed in a circle with a radius r.  Since the direction of motion is constantly changing the object must be accelerating and that this centripetal acceleration (a_r) is always directed radially.  The equation used to calculate this acceleration is a_r = v²/r.  

        The force needed to keep an object moving in a circular pattern is called the centripetal force and is also directed inwardly to the center of the circle.  The equation is F_c = mv²/r.

        Newton's law of universal gravitation states that all particles are mutually attracted toward each other because of gravity.  This force of attraction is inversely proportional to the distance be them and directly proportional to their massed.  The equation is F_g = Gm₁m₂/r².  The constant G is called the gravitational constant and is equal to 6.67 x 10^-11 Nm²/kg².

Sample Problems

1. Centripetal force and acceleration

2. Daredevil

3. Orbital motion

Chapter 6 -Work and Energy

Objectives

Basic Concepts 

            Whenever a force is applied to an object as it moves through some distance work is being done on that object.  The component of the force that is responsible for the work is that which is parallel to the direction of travel.  The equation W_k = Fx cos f , where f is the angle between the force and the direction of motion, is used quantify the value for work.

        Energy is defined as the ability to do work.  Energy can easily be broken up into different types (light sound, electric, chemical, etc.).  In this chapter we will only use the distinction between kinetic and potential energies.  Translational kinetic energy is the energy an object possesses because of its motion along a path.  It is given by the equation  KE = 1/2 mv².  Potential energy is stored energy.  In this chapter we will confine ourselves to gravitational potential energy (GPE0 which is given by the equation GPE = mgh.  The variable h stands for the height above  selected reference point.  In later chapters will consider elastic potential energy (1/2 kx²) as well as others.

        The law of conservation of energy states the total amount of energy in a isolated system is constant.  The law is valid even if friction is present.  This does leave however the possibility of the total amount of energy existing in different  and changing forms.

        The term used to define how fast energy is being used or applies is power.  The equation is given as P = W_k/t. and it has the SI unit of Watts.

Sample Problems

1. Conservation of mechanical energy

2. Energy Conversion

3. Work-Energy theorem

4. Frictional Forces

Chapter 7-Linear Momentum 

Objectives

Basic Concepts 

            The product of mass and velocity is defined as momentum (r = mv).  It is a vector and therefore must be added together as such using xy components.  Any force applied to an object will accelerate that object according to Newton, which means its momentum must also be change (because of the change in the velocity).  This relationship can be seen in the following equation  Ft = Dr = mv - mv_o.  The quantity Ft is defined as the impulse of the force applied.

        The law of conservation of momentum states that the total amount of momentum in an isolated system will remain constant.  When objects collide or explode, the use of the conservation law is very useful.  It can be stated the total momentum of the objects before the collision must be equal to their total momentum after the collision.

    There are 3 primary types of collisions. The first is an elastic collision, which means that not only is momentum conserved, but so is kinetic energy. Molecular collisions are believed to be of this type.  A more common type of collision is called inelastic.  In an inelastic collision momentum is conserved but kinetic energy is not.  In a perfectly inelastic collision the two colliding objects stick together after the collision.

Sample Problems

1. Conservation of Momentum-Recoil

2. Conservation of Momentum-Collision