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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