PHYS 111-6 Notes for the Final Examinationp. 1
Final Exam: Tuesday, December 18, 2007 from 2:00 PM to 4:00 PM in room W3-42.
Review the study notes and homework for the hour tests and quizzes given during the semester. Be sure to review material relating to test questions that you had trouble with. Also read the Summary that appears at the end of each chapter. References to chapter examples that relate to specific formulas or concepts are given in each Summary. There are many exercises and problems at the end of each chapter; try to do some of the ones that were not assigned for homework. A formula sheet will be provided with the final examination. However, it is your responsibility to know the meaning of the symbols in the formulas and what the formulas are used for. Also, be sure that you know the units of the quantities that appear in the formulas. You should know how to convert between common metric units (for example, cm and m, g and kg, cm2 and m2) and other common units (such as seconds and minutes, minutes and hours).
Chapter 1 Introduction and Mathematical Concepts
Summary is on p. 19. Know the difference between scalars and vectors. Know how to add and subtract vectors graphically. Know how to find the components of a vector and how to do addition of vectors by components.
Chapter 2 Kinematics in One Dimension
Summary is on p.51. Know the definitions of speed, velocity and acceleration. Know how to solve word problems involving the equations of kinematics for constant acceleration. Know what the acceleration due to gravity is and how to solve problems involving free-fall motion.
Chapter 3 Kinematics in Two Dimensions
Summary is on p.79. Know the definitions of velocity and acceleration for two dimensions. Know how to solve projectile motion problems.
Chapter 4 Forces and Newton's Laws of Motion
Summary is on p.123. Know the distinction between mass and weight. Know how and when to use the formula for converting between mass and weight. Know that the British Engineering unit pound (lb) measures weight (or force) and that the metric unit kilogram (kg) measures mass. Example: What is the weight of a 10 lb object? What is the weight of a 10 kg object? Answers: A 10 lb object weighs 10 lb (do not multiply by g). A 10 kg object has weight
Know how to state each of Newton’s three laws of motion. Know the definition of inertial frame of reference. Know how to identify action-reaction pairs of forces.
Be familiar with the different types of forces: normal force, tension force, friction force, gravitational force. Know how to find the apparent weight of an object in an accelerating elevator. Know the difference between static and kinetic forces of friction and how to use Equations 4.7 and 4.8.
Be familiar with Newton’s law of gravity: and the meanings of the symbols in this formula.
Know how to solve problems involving Newton’s first and second laws of motion. These include problems involving objects being pushed or pulled across surfaces or objects sliding up or down inclines.
Chapter 5 Dynamics of Uniform Circular Motion
Summary is on p.154. Know what is meant by the term period for uniform circular motion and how the speed v of an object in uniform motion around a circle of radius r is related to the period: . Know that an object in uniform circular motion has an acceleration directed toward the center of the circular path of motion. This acceleration is called centripetal acceleration. Be familiar with the formula for centripetal acceleration:.
Know how to find the proper banking angle for banked curves (Equation 5.4). Be able to recognize Equations (5.5) and (5.6) as formulas for the speed and period, respectively of an object in a circular orbit.
Chapter 6 Work and Energy
Summary is on p.186. Know how to find the work done by a constant force and the MKS units of work (J). Know that kinetic energy (Equation 6.2) is the energy of motion and how to use the work-energy theorem (Equation (6.3)) to solve problems in mechanics.
Be familiar with gravitational potential energy: where h is the height of an object of mass m relative to an arbitrary reference level.
Know what is meant by the terms conservative force and nonconservative force.
Know that total mechanical energy of a system is the sum of its kinetic and potential energies: . Be familiar with the work-energy theorem: , where Wnc is the work done by nonconservative forces acting on a system. E0 is the initial total mechanical energy of the system and Ef is its final total mechanical energy. Know that when Wnc = 0 the total mechanical energy of a system is conserved and how to use conservation of energy to solve problems in mechanics where this principle applies.
Know what is meant by the term average power and how it can be calculated (Equations (6.10) and (6.11).)
Know that the work done by a variable force is the area under a force versus distance graph. (See Section 6.9.)
Chapter 7 Impulse and Momentum
Summary is on p.215. Know the definitions of impulse and momentum and their associated units. Be familiar with the impulse-momentum theorem (Equation (7.4)) and the principle of conservation of momentum (Equation (7.7b)).
Know the meanings of the terms elastic collision and inelastic collision and how to solve collision problems in one dimension.
Chapter 8 Rotational Kinematics
Summary is on p.239. Know the definition of an angle measured in radians, Equation (8.1). Know the definitions of angular velocity and angular acceleration, Equations (8.2) and (8.4) and their associated units.
Know how to solve word problems involving the equations of rotational kinematics for constant angular acceleration.
Know the relationships between angular variables and tangential variables, Equations (8.1), (8.9) and (8.10).
Know the difference between centripetal acceleration (Equation (8.11)) and tangential acceleration.
Chapter 9 Rotational Dynamics
Summary is on p.276. Know the definition of the lever arml of a force and the definition of the torque due to a force F about a given axis: .
Be familiar with the equations that must be satisfied for a rigid body in equilibrium:
and how to use these equations to find unknown forces or distances for a rigid body in equilibrium.
Be familiar with the definition of the moment of inertiaI of a body (or system of particles) about a fixed axis O and the associated units. Know what property of a body (or system of particles) the moment of inertia measures.
Know how to use Newton’s second law for rotational motion: to solve rotational motion problems for rigid bodies rotating about a fixed axis.
Be familiar with the formulas for rotational work and kinetic energy, Equations (9.8) and (9.9). Know how to use conservation of energy to solve problems involving rotational motion.
Be familiar with the concept of angular momentum (Equation 9.10) and how to use the principle of conservation of angular momentum to solve problems involving rotational motion.
Chapter 10 Simple Harmonic Motion and Elasticity
Summary is on p.311. Be familiar with Hook’s law for an ideal spring: where F is the force exerted by the spring due to its extension x from its equilibrium length. k is the spring constant or force constant of the spring, with MKS units N/m.
Know that a mass m attached to the end of a spring and subject only to the spring’s force will execute simple harmonic motion when it moves. Know the definitions of amplitude, period, frequency and angular frequency in simple harmonic motion. Be familiar with the period of simple harmonic motion: .
Know what a simple pendulum is and be familiar with the formula for its period: , where l is the length of the pendulum measured from its point of support to the center of the pendulum bob, which is assumed to be a small object. Know that for small amplitudes the simple pendulum executes simple harmonic motion.
Know what driven harmonic motion is and that mechanical resonance (motion with maximum amplitude) occurs when the frequency of the driving force matches the natural frequency of vibration of the harmonic oscillator.
Know what is meant by the terms stress and strain in elastic deformation and be familiar with the formula that relates tensile stress to tensile strain: , where force F is applied to an object of initial length L0 and cross-sectional area A. L is change in length of the object because of the applied force and Y is a constant called Young’s modulus.
Chapter 11 Fluids
Summary is on p.350. Know the definition of mass density as mass per unit volume: with units kg/m3. Know the definition of pressure as force per unit area: with units N/m2 or Pa (pascals).
Know how to find the pressure at a certain depth in a static fluid. See Conceptual Examples 3, 4 and 5.
Know the distinction between gauge pressure and absolute pressure: Gauge pressure is the amount by which a pressure P differs from atmospheric pressure. The absolute pressure is the value of the pressure P itself. Note that gauge pressure can be either positive or negative.
Know the following principles:
Pascal’s Principle: Any change in pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls.
Archimedes’ Principle: An object placed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.
Be familiar with the equation of continuity for an incompressible fluid, Equation (11.9).
Be able to recognize Bernoulli’s equation, Equation (11.11).
Chapter 12 Temperature and Heat
Summary is on p.386. Be familiar with the common temperature scales and how to convert between them.
Be familiar with problems involving linear and volume thermal expansion and Equations (12.2) and (12.3).
Know how to use Equation (12.4): to solve problems involving heat and temperature change. Specific heat values will be provided as needed.
Know what a phase change of a substance is, and that during a phase change the temperature of the substance remains constant. Be familiar with Equation (12.5) for calculating heats associated with melting and vaporization.
Chapter 16 Waves and Sound
Summary is on p.501. Know that there are essentially two different kinds of waves: transverse and longitudinal. Know how each is identified:
Transverse wave: The wave vibrations are perpendicular to the direction of motion (also called the direction of propagation) of the wave. Examples: waves on a string, radio waves.
Longitudinal wave: The wave vibrations are parallel to the direction of motion of the wave. Examples: compressional waves in a spring, sound.
Know that a periodic wave consists of cycles or patterns that are produced over and over again by the source of the wave. Know that the amplitudeA of a wave is the maximum excursion of a particle of the medium from the particle’s undisturbed position. Know that the wavelength of a wave is the distance along the direction of motion of the wave occupied by one cycle. Know that the period T of the wave is the time required for the completion of one cycle of the wave, or equivalently the time it takes the wave to travel a distance of one wavelength. Know that the frequency f of the wave is the number of cycles that pass a given point along the path of motion of the wave per unit time and that the units are cycles/second or hertz (Hz). Also know that .
Know the definition of the intensity of a sound wave: , where P is the rate of flow of wave energy per unit time through an area A that is perpendicular to the direction of motion of the wave. The units of intensity are watts/m2.
Know that the intensity of spherically uniform radiation varies as the reciprocal square of the distance r from the source, given by , where P is the power of the source.
Be familiar with the threshold of hearing: . Also know that the intensity level (in decibels) is given by , where I is the intensity of the sound and I0 is the threshold of hearing. One decibel is approximately the smallest change in loudness that an average listener with healthy hearing can detect.
Know that if the intensity level increases by 10 dB, the new sound seems approximately twice as loud as the original sound.
Also refer to the study notes for each of the six tests given during the course. These are available at the Instructor’s website: