Download THEORETICAL SUBJECTS General Physics Course –Part I 1 term

THEORETICAL SUBJECTS
General Physics Course –Part I 1st term (ETTI)
Prof. Dr. Ing. Coriolan TIUȘAN
UNITS, PHYSICAL QUANTITIES AND VECTORS
1) What is a physical quantity and what implicates the measuring of a physical quantity?
Give some examples of physical quantities indicating the corresponding units of
measure and their nature: scalar or vector.
2) Give the definitions of scalar and vector quantities. Illustrate the relevant elements of
a vector quantity. Give examples of scalar and vector physical quantities.
3) Vector addition and vector subtraction: give the definitions, the graphical
representation (case of two vectors). Illustrate and discuss the case of many vectors,
for vector addition. Are the vector additions and vector subtraction commutative laws,
justify analytically and graphically?
4) Using vector components represent graphically and calculate the vector sum in a bidimensional and tri-dimensional space.
5) Vector multiplication operations: define and represent graphically:
a. the multiplication by a positive/negative scalar.
b. the scalar product.
c. the vector product.
6) Illustrate the analytical representation of a vector in 2D and 3D space.
7) Using the analytical representation of vectors, define the sum and the difference of
two vectors.
8) Using the analytical representation of vectors, define the multiplication operations:
a.
b.
c.
the multiplication by a positive/negative scalar
the scalar product
the vector product
KINEMATICS
1) Define the particle approximation in kinematics. In which situation it represents a
satisfactory approach for solving a problem of kinematics?
2) Considering the motion in one dimension, give the definition, indicate the unit, make
a relevant figure and the corresponding x-t graph for:
a.
b.
c.
d.
The average velocity.
The instantaneous velocity.
Explain the difference between speed and velocity.
Discuss relative the sign of x-velocity and x -displacement.
3) Considering the motion in one dimension, give the definition, indicate the unit, make
a relevant figure and the corresponding v-t graph for:
a. The average acceleration
b. The instantaneous acceleration
c. Discuss relative the sign of x-acceleration and x-velocity.
4) Write the equations of motion corresponding to the case of unidimensional motion
with constant acceleration. Give the analytical expression for x(t), v(t) and a(t) and the
graphical representations: x-t graph, v-t graph, a-t graph.
5) Define the free falling illustrating with a relevant figure and give the value of the
acceleration g due to the gravity. Discuss the sign of g with respect to a vertical
referential.
6) Write the equations of motion in case when the acceleration depends on time: velocity
and position by integration in case of unidimensional motion.
7) Give the definition (analytical representation) and make the relevant describing figure
for the position vector of a particle in a 3D space.
8) Using the analytical representation of a vector in a 3D space define and make the
corresponding graphical representation for:
a. The average and the instantaneous velocity vectors
b. The average and the instantaneous acceleration vectors

9) Consider the case of a particle moving along a curved path with constant v . Even if
the magnitude of velocity is constant, its direction changes. Which component of the
acceleration (parallel at or perpendicular an to the path) is non-zero? Make a sketch.

10) Consider the case of a particle moving along a curved path with non- constant v .
Indicate the direction of the total acceleration with respect to the velocity in two
distinct situations: the speed is increasing and the speed is decreasing.
11) Define the uniform and the non-uniform circular motions. Illustrate graphically and
give analytical expression for velocity and accelerations (radial, centripetal) in
uniform and non-uniform circular motions.
DYNAMICS
1) Define the concept of force in dynamics.
2) Enounce the Newton’s laws of dynamics:
a. First Newton’s law.
b. Second Newton’s law.
c. Third Newton’s law.
3) In agreement with the Newton’s laws, explain the conditions for a body to be in
equilibrium (rest or movement with constant velocity) in case when subjected to many
forces. In what situation the body moves with:
a. constant acceleration
b. time dependent acceleration
4) Enounce the law of universal attraction and give analytical expression of the
corresponding force between two bodies with masses m and M spaced by r.
5) Within the framework of the universal attraction define the gravitational force, the
gravitational acceleration or the intensity of the gravitational field (g0).N Deduce and
discuss the variation of g with the altitude.
6) Considering the case of parallelepiped body on a plane surface:
a. Define the static and the dynamical friction.
b. Indicate on figure and give analytical expressions for the static and the
dynamic friction forces.
7) How do the friction and viscosity forces act with respect to the velocity vector a
moving particle? Which of them depends on the speed and how (analytical
expression)?
WORK AND ENERGY. CONSERVATION LAWS
1) Give the definition of work in mechanics. Give the analytical expression of work in
case of constant or varying with position force (integral definition). Consider the work
of a force making an angle to the displacement. Which is the expression of the work in
this case? Discuss the sign of the work. Total work of many forces acting on a body.
2) Define the kinetic energy (give analytical expression) and enounce the work-energy
theorem.
3) Define the mechanical power: average and instantaneous power. Units of measure for
power. Relation power-velocity.
4) Define the concept of potential energy. Give the analytical expression of the:
a. gravitational potential energy.
b. potential energy of an elastic field (spring).
5) In case of gravitational and elastic forces, give the corresponding conservation law for
the total mechanical energy, indicating the analytical expression of the corresponding
potential energy.
6) Write the general energy conservation law when other forces than gravity or elastic
forces act on a body.
7) Give the definition of a conservative force and enounce some of main properties of the
work done by a conservative force.
8) Give the definition of a non-conservative force and give some examples. Which is the
general conservation law in case when conservative and non-conservative forces act
simultaneously on a moving body?
MOMENTUM, IMPULSE, COLLISIONS
1) Give the definition of the particle linear momentum. Furthermore, defining the
impulse of the net force enounce the Newton’s second law in term of momentum.
2) Define the concepts of: internal forces, external forces, isolated system. Enounce the
principle of conservation of momentum in case of two or many interacting particles.
3) Define the elastic, the inelastic and the completely inelastic collision. Make relevant
sketches.


4) Consider two moving particles of masses m1 and m2 and initial velocities v1 and v2 .
The two particles collide. Write the momentum conservation law in a vector form and
project on x, y axis. In case of the elastic collision write the corresponding kinetic
energy conservation law.
5) Give the definition for the center of mass. How does the total momentum for an N
particle system can be described using the notion of center of mass? Considering the
movement of the center of mass, enounce the Newton’s second law in case of a
collection of particles acted by external forces.
DYNAMICS OF ROTATIONAL MOTION
1) Define the corresponding physical quantities for the rotational motion:
Angular velocity (average, instantaneous)
Angular acceleration (average, instantaneous)
2) Write down the motion’s equations in case of rotational movement with constant
acceleration (  (t ) ,  (t ) laws). Discuss the correspondence with the linear motion
with constant (linear) acceleration.
3) Define the moment of inertia and the rotational kinetic energy of a rotating rigid
body.

4) Define the torque due to a force F acting on a rigid body. What kind of physical
quantity is the torque (scalar or vector)? Illustrate schematically the right hand
rule.
5) Write down the rotational analogy of the Newton’s second law for a rigid body,
expressed in terms of total torque and inertial moment.
6) Give the analytical expression of the work done by torque acting on a rigid body.
Define the instantaneous power and discuss the analogy with the translational
motion.
7) Give the definition of the angular momentum for rotational movement of a rigid
body. Which is the corresponding physical quantity in the translational motion?
8) Enounce the angular momentum - torque theorem. Which is the analog expression
in case of translational motion?
9) Enounce the second principle of dynamics for rotating rigid, in terms of angular
momentum. Write down the conservation conditions for the angular momentum in
the rotational motion of a rigid body. Which are the analog expressions in case of
translational motion?
10) Write down the two general conditions of equilibrium in case of a rigid body
having translational and rotational movement? Illustrate with some relevant
figures/sketches.
11) Define the center of gravity of a rigid body. Relationship with the total torque.
12) Write down the general form of the Hook’s law giving the definition of stress and
strain. Expressions of Hook’s law in cases of tensile and compressive stress and
strain.
FLUID MECHANICS
1) Define the pressure in a fluid. Unit of measure.
Define the hydrostatic pressure. How this pressure does varies with the depth
in the fluid. Give examples from real life.
Define the atmospheric pressure. How the atmospheric pressure does vary with
the altitude?
2) Enounce the Pascal law for fluids and explain, as application, the principle of the
hydraulic lift.
3) Enounce the Bernoulli’s law and within its framework explain the lift of the airplane
wing. Explain the curved trajectory of a moving spinning ball.
PERIODIC MOTION. OSCILLATIONS.
1) Define the periodic motion and explain which the physical condition under which
oscillations occur is.
2) Define the main characteristics of the periodic motion: amplitude, period, frequency,
angular frequency. Units of measure and inter-dependency.
3) Define the simple harmonic motion (SHM). Which is the equation of movement of the
SHM? Define the main characteristics of the SHM:
a. Frequency and period in SHM
b. Displacement, velocity and acceleration in SHM. Graphical representations of
x(t), v(t), a(t).
c. Kinetic, potential and total energy in SHM. Graphical representations of
K(t),U(t), E(t).
4) What kind of motion has the simple pendulum at small amplitudes? Deduce the
expression of the frequency, period, and angular frequency for this motion. What is a
physical pendulum? What real life applications you can mention for these oscillating
pendulums?
5) Give the definition of damped oscillations. Which is the origin of damping? Applying
the 2nd principle of Newton, write/deduce the differential equation describing the
damped oscillations in case of a damping force simply proportional with the velocity
of the oscillating body. Give the general solution of the damped oscillator and
represent graphically x(t). What happen with the total energy during a damped
oscillation?
6) For the damped oscillations, define the following quantities:
a. The damping logarithmic decrement
b. The relaxation time
c. The quality factor
7) Define a forced oscillation, giving one (some) examples from real life. Define the
resonance and discuss what happens with the amplitude of the forced oscillations at
resonance. Applying the 2nd principle of Newton, write/deduce the differential
equation describing the damped oscillations of on an oscillating system of mass m
whose natural oscillations are driven by a restoring force F=-kx in case of a damping
force simply proportional with the velocity of the oscillating body : Fx=-bvx,
submitted to a sinusoidal driving force Fd  Fmax sin(d t ) . The amplitude of the forced
Fmax
oscillations is given by the expression: A 
. Discuss
(k  md 2 ) 2  b 2d 2
graphically the dependence of A on the ratio d /  . Define the resonance
phenomenon and discuss its consequences in real life and technics.
8) Considering two oscillations x1 (t )  A1 sin(1t ) and x2 (t )   A2 sin(2t ) , define the
phenomenon of beats, specific for oscillations and waves. What happened with the
amplitude in time? Represent graphically x(t) of resulting oscillation and
deduce/discuss its amplitude and angular frequency.
MECHANICAL WAVES/ ACOUSTICS
1) Define a wave and give some examples. What is a mechanical wave? Define and
make graphical representation for a transverse and a longitudinal wave. Define the
wave front and classify waves as a function of the shape of the wave front. Give some
common characteristics of waves, independent of their type.
2) Define and represent graphically a periodic wave (i.e sinusoidal wave). Which is the
relationship with the simple harmonic motion of the medium’s particles in case of
transverse or longitudinal waves. Define the wavelength and give the relationship
between wavelength, period or frequency and the wave speed.
3) Give the mathematical description of a wave. Which are the general characteristics of
any periodical wave? Which is the wave equation for a transverse wave moving along
the +x direction, and of a wave moving along the –x direction? For one of these cases,
illustrate by graphs y(x) at t=0 and y(t) at x=0 the wave equation y(x,t) , periodic both
in time and space. In these graphs, define the wavelength  and the period T. Define
the wave speed of a propagating wave and explain why this is also called the phase
speed of the wave.
4) For a transverse wave propagating along the +x direction y ( x, t )  A cos(kx  t )
deduce the expression of the particle velocity vy(x,t), the particle acceleration ay(x,t) .
5) Give the general expression for the propagation speed of a of a mechanical wave. Give
the particular expressions for transverse waves in vibrating strings and longitudinal
waves in fluids, describing in each case the corresponding physical quantities from the
definition equations.
6) Define the wave intensity. Unit of measure. Discuss the intensity dependence on the
distance from the source (decay law) in case of spherical isotropical propagation and
in case of uni-directional propagation (the last case only qualitative).
7) What happen with a wave when it reaches the boundary of the medium? What happen
when two or many waves pass through the same area at the same time? Enounce the
principle of superposition for waves.
8) Define a standing wave and illustrate some conditions under which a standing wave
may be created. Define the characteristics of a standing wave: node and antinode. Give
the analytical expression of a standing wave and discuss the mathematical conditions
for nodes and antinodes. Does standing wave transport energy? Discuss.
9) Define the normal modes of a vibrating string of length L fixed at both ends. Which is
the fundamental frequency and which are the harmonics? Represent graphically the
fundamental and few harmonics of the string L. Describe the utility of the Fourier
analysis in case of complex standing waves. If the fundamental frequency of a
1 F
, where F is the elastic
vibrating string L is given by the equation: f1 
2L 
restoring force in the string and  its linear density, explain the tone/pitch of the
sounds produce by string instruments: in which way the grave and high tones can be
produced by an instrument with strings (e.g. guitar)?
SOUNDS AND HEARING
1) Define the sound waves and indicate the way they propagate in a medium. Define the
audible frequency range. How do we call the waves with frequency above and below
the audible range?
2) Write the wave equation corresponding to a longitudinal wave and discuss the
significance each physical quantity. Compare with the case of transverse waves.
3) Write down the analytical expressions for the wave equation and the pressure
fluctuation induced by the wave propagation in a medium. Represent the two
quantities y(x,t) and p(x,t) graphically and discuss the relative position of nodes and
antinodes. Which is the maximum value of the pressure modification in a medium
induced by a passing longitudinal wave?
4) Define the following notions: harmonic content of a sound wave, timbre, noise and
white noise.
5) Write down the analytical expression for a sound wave in a fluid explaining the
corresponding physical quantities in the equation.
6) Explain the working principle and calculate the corresponding wavelength   v / f
explaining the minimum object size one can probe in both cases for:
a. the sonar working with sounds at f=262Hz and
b. for the ultrasonic imaging at f=5MHz in human bodies mainly constituted by
water. The speed of sound in water is v  B /  =1420ms/s at t=20oC.
 RT
where =1.40
M
represents the ratio of heat capacities, T- the absolute temperature in Kelvin, M- the
molecular mass of the gas. Considering that the mean molecular mass of air, mainly
constituted by N2 and O2, is M=28.8 *10-3 Kg/mol, calculate the wavelength of the
7) The speed of sound in a gas is given by the equation: v 
sound propagating at 20oC corresponding to the frequency limits of the audible range:
f=20 Hz and at f=20 kHz.
8) Define the intensity of the sound and explain how this is related with the displacement
amplitude y(x,t) and the pressure p(x,t) variation induced by the wave propagation .
Explain the significance of the physical quantities appearing in the alternative
p 2
1
 B 2 A2  max . Explain why for
equations defining the sound intensity: I 
2
2v
similar intensities a low frequency woofer has to oscillate at much larger amplitude
than a high frequency tweeter to produce same sound intensity.
9) Which is the power law describing the sound intensity variation with the distance from
the emitting source in case of waves emitted in all directions isotropically? In
comparison, how the sound intensity does vary if the sound is emitted or directed only
along one direction? Define the phenomenon of sound reverberation.
10) Justify the logarithmic scale for the sound intensity. Define the sound intensity level
and the corresponding unit and give some examples of sound intensity levels
corresponding to various sources.
11) Define the standing sound waves and the characteristics of normal modes. Discuss the
relationship between the nodes and antinodes in displacement and pressure in case of a
standing sound wave.
12) Discuss the forced oscillation phenomenon in case of sound wave and define the
resonance regime. Figure schematically the shape of a resonance curve A(f) in case of
a system with many normal modes: e.g. open organ pipe connected at one end to a
speaker emitting sounds at variable frequency f. What happened in a system with zero
damping at acoustic resonance?
13) Consider
two
waves
described
by
the
equations:
y1  A1 sin(1t  1 ) and
y2  A2 sin(2t  2 ) . Using the phasor representation, make the vector (phasor)
diagram and calculate the square amplitude A2 of the resulting wave described by
y  y1  y2  A sin(t   ) . Analyze the situation where the average value A2 is
different from zero and, in this case write the resulting wave intensity, as a function of
the intensities of the corresponding overlapping waves I1 and I2. In this situation, give
the definition of the coherent waves. Write down the mathematical conditions verified
by the phase-shift   2  1 in case of constructive and destructive interference of
waves. Which is the wave intensity of resulting wave, corresponding to constructive
and destructive interference? Based on interference principle explain how one can
cancel the sound intensity in noisy environments by adding additional sound/noise
sources.
14) Explain the Doppler effect of sound waves. Discuss the two situations:
a. Moving listener with the speed vL and a stationary sound emitting source.
b. Moving source with vs and fixed listener (particular case of moving source
with speed vs and moving listener with speed vL).
c. Explain the working principle of the radar device used by the police, based on
Doppler effect.
d. Considering the Doppler effect of electromagnetic waves explain the
signification of the red shift of the radiation emitted by the galaxies.
15) Explain the origin of shock waves and define the speed regime produced when a
sound source moves in a fluid with the speed v in which the speed of sound is vs .
What is the sonic boom? Illustrate schematically the situations corresponding to v  vs
, v  vs and v  vs . Define the Mach number and its relationship with the angle of the
cone formed by the shock waves in a 3D representation. Which is the explanation of
the cracking noise produced by a circus whip?
___________________________________ Total = 86 subjects