Αξιολόγηση εκπαιδευτικών - ΠΔ 152 / 2013 - Ενημερωτική προβολή
EF 152 Final Exam, Spring, 2012 The equation sheets may ......EF 152 Final Exam, Spring, 2012 Page 9...
Transcript of EF 152 Final Exam, Spring, 2012 The equation sheets may ......EF 152 Final Exam, Spring, 2012 Page 9...
EF 152 Final Exam, Spring, 2012 Page 1 of 10
Uniform Circular Motion an – centripetal acceleration v – speed ρ – radius of curvature ω – rotational speed T – period f – frequency
– angle
(any curve)
Kepler’s Third Law
Satellites
rearth = 6.378x106 m mearth = 5.976x1024 kg
Stress and Strain
Universal Law of Gravitation
G = 6.67x10-11 N-m2/kg2
Factor of Safety (FS)
Fluids p – pressure h – height ρ – mass density v – velocity K – empirical constant A – area d – depth p0 – pressure on top of fluid Conservation of Mass (Continuity)
Bernouilli’s Equation
Lift
Pressure in a fluid
Density of Water 62.4 lb/ft3 1000 kg/m3
Atmospheric Pressure 1 atm = 101.3 kPa 1 atm = 14.7 psi
Stokes’ Law Sphere through fluid for laminar flow
Poiseuille’s Equation
η – viscosity L – characteristic length v – velocity ρ – mass density R – sphere radius
Conversions 1 ft3 = 7.48 gal 1 m3 = 1000 L
The equation sheets may be removed when the test b egins Guidelines:
• Assume 3 significant figures for all given numbers unless otherwise stated • Show all of your work – no work, no credit • Write your final answer in the box provided - include units for all answers • If you finish with less than 5 minutes remaining, remain seated until the end of the
exam and all exams are collected.
EF 152 Final Exam, Spring, 2012 Page 2 of 10
Wave Equation v – wave velocity A – amplitude k – wave number ω – angular frequency λ – wavelength f – frequency
v is positive if sign of ω is negative
Harmonic Motion ω – angular frequency A – amplitude k – stiffness m – mass δ – phase angle x0 – initial displacement v0 – initial velocity T – period f – frequency
Pendulums
Simple:
Physical:
Parallel Axis Theorem
Wave Speed Cables, Ropes, etc. T – tension µ – mass per unit length E – modulus of elasticity ρ – mass density
Transverse:
Longitudinal:
Wave Energy, Power, Intensity E – energy I – intensity P – power
- average power
Natural Frequencies: λ – wavelength L – Length n – harmonic T – tension µ – mass per unit length f – frequency v– wave velocity in medium String
Air Columns
closed pipe:
n= 1, 3, 5…
open pipe:
n= 1, 2, 3…
Speed of Sound in Air
T in °C
Doppler Shift f0 – frequency f′ – shifted frequency v – velocity of medium vS – velocity of source vL – velocity of listener
Positive is from listener to source.
Beat Frequency: | f2 – f1 |
Sound Level I0 – reference intensity, 1x10-12 W/m2 I – intensity
Light Waves
Law of Reflection
Index of Refraction
Law of Refraction
Light Wavelength
Total Internal Reflection
EF 152 Final Exam, Spring, 2012 Page 3 of 10
Work of Thermal Systems
Isobaric (constant pressure)
Isochoric (constant volume)
Isothermal (constant temp)
Adiabatic (∆Q = 0)
Heat Q– heat c – specific heat κ – thermal conductivity R – thermal resistance Heat Capacity
Thermal Conductivity
Thermal Resistance
Thermal Resistance, Series
Thermal Resistance, Parallel
Thermal Expansion Linear
Linear, Stresses
Volumetric
Ideal Gas Law
R = 8.314 J/(mol-K) Avogadro’s Number: 6.02x1023 Standard Pressure and Temp 273K 1.00 atm (101.3kPa)
1st Law of Thermodynamics U – internal energy W – work done by thermal
system Q – heat flow into thermal
system
Water Properties c = 1 cal/(g-°C) = 4.186J/(g-°C) Lf = 79.6 cal/g Lv = 540 cal/g ρ = 1 g/cm3 = 1 kg/L = 1000 kg/m3 = 62.4 lb/ft3 Lf = Latent heat of fusion Lv = Latent heat of vaporization
Conversions 1 cal = 4.186 J 1 BTU = 1055 J 1 hp = 0.707 BTU/sec 1 L = 1000 cm3
1 m3 = 1000 L
Entropy
Ideal Gas
Refrigerators General K – coefficient of performance H – heat current P – power input
Carnot
Molecular Thermal Physics m – mass of a molecule M – molecular mass n – number of moles N – number of molecules k – Boltzmann constant = 1.38065 × 10-23 J/ K
Efficiency General
Otto Cycle r – compression ratio
Carnot Cycle
EF 152 Final Exam, Spring, 2012 Page 4 of 10
Constants me=9.109x10-31 kg mp=1.673x10-27 kg mn=1.675x10-27kg
k = 9x109
ε0 = 8.854 ·10-12
e = -1.6022 ·10-19 C (electron charge) eV = 1.6022·10-19 J (electron volt) Coulomb’s Law (electrostatic force)
Electric Field – point charge
- unit vector from charge to a location
Potential energy - point charges
Potential
Potential of a set of point charges
Potential difference between two parallel plates
Capacitance
Capacitance – parallel plates
Capacitance – energy storage
Capacitors in series
Capacitors in parallel
Resistors in series
Resistors in parallel
Current
Voltage, Resistance, Current, Power V=I·R P=I·V Kirchhoff’s Rules
for a closed loop
for a junction
Magnetism
Magnetic force on moving charged particle
Magnetic field of a moving charged particle
Magnetic Field of a straight wire
Magnetic field along the axis of a looped wire
a – radius of the loop x – distance from the center of the loop to point of interest on the axis. I – current in the wires N – number of loops
in a vacuum
EF 152 Final Exam, Spring, 2012 Page 5 of 10
Remove the 2 equation sheets, leaving the exam questions stapled together. CLEARLY PRINT the information below. Name: __________________________________________________ EF 152 Section: ____________ NetID: ____________________________ (your computer login, NOT your student #, e.g. lazydog1)
1. (1 pt) How must the intensity of a sound be changed to cut the loudness in half?
a. 1/100
b. 1/10
c. 1/2
d. 1/√2
2. (1 pt) What is the change in internal energy for an adiabatic process?
a. +Q
b. –Q
c. +W
d. –W
e. 0
3. (2 pt) A uniform beam 10.0m long, weighing 400N rests symmetrically on two supports, A and B, 4.0m apart.
Todd weighs 800N and walks along the beam from A to B. How far beyond B can he walk before the beam
begins to tip?
a. 1m
b. 2m
c. 3m
d. 4m
4. (6 pts) A bracket hangs from a wall and is loaded as shown. Calculate the magnitude of the force supported by
the pin at A. Neglect the weight of the bracket. A separate, complete FBD is required for full credit.
EF 152 Final Exam, Spring, 2012 Page 6 of 10
5. (6 pts) Josh is on the International Space Station making 0.652 revolutions per hour in its orbit around the
earth. Assuming a circular orbit, how high is this satellite above the surface of the earth?
6. (6 pts) A proposed elevator in Estabrook is suspended by a steel cable with cross-sectional area 3x10-4
m2 and
an ultimate strength of 9.25 x 108 Pa. If the elevator weighs 10kN, how many 70kg students can the elevator
hold for a minimum factor of safety of 18?
7. (6 pts) A styrofoam buoy is held completely submerged in water by a rope. The volume of the buoy is
0.045 m3. What is the tension in the rope? ������ = 180kg/m�
A separate, complete FBD is required for full credit.
EF 152 Final Exam, Spring, 2012 Page 7 of 10
8. (6 pts) Megan is using sewing machine and notices that the point of the needle moves in simple harmonic
motion with a frequency of 8.5 Hz. At t=0 its position and velocity are +1.2cm and -0.7cm/s, respectively. Find
the acceleration of the needle at t=0.5 seconds.
9. (6 pts) Patrick ties a rope to a post and finds several frequencies at which he can oscillate the other end of the
rope so that a light clothespin 1.25 ft from the post doesn’t move. If the speed of the wave is 4.3 ft/s, what is
the fundamental frequency of this oscillation?
10. (6 pts) A bat flies toward a wall, emitting a steady sound of frequency 2000 Hz. The bat hears its own sound
plus the sound reflected by the wall. If the bat is flying 22 m/s, what beat frequency does it hear? The speed
of sound in air is 343 m/s.
EF 152 Final Exam, Spring, 2012 Page 8 of 10
11. (6 pts) Shane strikes a brass rod at one end. Patrick hears the sound at the other end 0.22 seconds later. How
long is the brass rod? ����� = 8600kg/m� ����� = 9x10��Pa
12. (6 pts) Geoff is designing an electronic circuit element made of 25x10-6
kg of silicon. The current going through
it adds energy at a rate of 8.3x10-3
J/s. His design does not allow any heat transfer out of the element. By how
much will its temperature increase in one minute? Specific heat of silicon is 705 J/kg-K.
13. (6 pts) Frances pours 0.375kg of coffee at 100°C into a well-insulated mug. How much ice at 0°C must be
added to achieve optimum drinking temperature of 92°C? Assume no heat is transferred to the mug.
EF 152 Final Exam, Spring, 2012 Page 9 of 10
14. (6 pts) Water at 80°C is brought to a boil and 20% of its original mass is converted to steam. If the total change
in entropy of the system is 9600 J/K, what was the original mass of water?
15. (6 pts) A Carnot refrigerator removes 950 J of heat. If the interior is 10°C and the outside is 35°C, how much
heat is transferred to the outside?
16. (6 pts) What must the charge (sign and magnitude) of a 1.65g particle be for it to remain stationary when
placed in a downward directed electric field of 720 N/C?
EF 152 Final Exam, Spring, 2012 Page 10 of 10
17. (6 pts) A circuit operates as shown. How much electrical energy does it consume during 2 hours?
18. (6 pts) For the system shown, the total charge is 47 μC. What is the potential drop from A to B?
19. (6 pts) An electron moves at 1.6x107 m/s as shown. Find the magnitude and direction of the magnetic field
this electron produces at point A, 2.0x10-6
m away.
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