EF 152 Final Exam, Fall, 2011 Page 1 of 10 EF 152 Final Exam, Fall, 2011 Page 2 of 10 The equation sheets may be removed when the test begins 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. Stress and Strain Factor of Safety (FS) Uniform Circular Motion a n centripetal acceleration v speed ρ radius of curvature ω rotational speed T period angle (any curve) Universal Law of Gravitation G = 6.67x10-11 N-m 2 /kg 2 Kepler s Third Law Satellites Harmonic Motion ω angular frequency A amplitude k stiffness m mass δ phase angle x 0 initial displacement v 0 initial velocity T period Parallel Axis Theorem Pendulums Simple: Physical: Speed of Sound in Air T in C Beat Frequency: f 2 f 1 Natural Frequencies: λ wavelength L Length n harmonic T tension µ mass per unit length v wave velocity in medium String Sound Level I 0 reference intensity, 1x10-12 W/m 2 I intensity Doppler Shift f 0 frequency f shifted frequency v velocity of medium v S velocity of source v L velocity of listener Positive is from listener to source. Wave Energy, Power, Intensity E energy I intensity P power - average power Fluids p pressure h height v velocity K empirical constant A area d depth p 0 pressure on top of fluid Conservation of Mass (Continuity) Density of Water 62.4 lb/ft 3 1000 kg/m 3 Atmospheric Pressure 101.3 kpa 14.7 psi r earth = 6.378x10 6 m m earth = 5.976x10 24 kg Stokes Law Sphere through fluid for laminar flow Wave Equation v wave velocity A amplitude k wave number ω angular frequency λ wavelength Air Columns one end closed both ends open Wave Speed Cables, Ropes, etc. T tension µ mass per unit length E modulus of elasticity Light Waves Law of Reflection Index of Refraction Law of Refraction Bernouilli s Equation Conversions 1 ft 3 = 7.48 gal 1 m 3 = 1000 L Poiseuille s Equation Transverse: Light Wavelength Total Internal Reflection Lift η viscosity L characteristic length v velocity R sphere radius v is positive if sign of ω is negative Longitudinal: Pressure in a fluid
EF 152 Final Exam, Fall, 2011 Page 3 of 10 EF 152 Final Exam, Fall, 2011 Page 4 of 10 Thermal Expansion Linear Linear, Stresses Volumetric Work of Thermal Systems Isobaric (constant pressure) Heat Q heat c specific heat κ thermal conductivity R thermal resistance Heat Capacity Constants m e=9.109x10-31 kg m p=1.673x10-27 kg m n=1.675x10-27 kg k = 9x10 9 Capacitance Capacitance parallel plates Ideal Gas Law Isochoric (constant volume) Thermal Conductivity ε 0 = 8.854 10-12 Capacitance energy storage R = 8.314 J/(mol-K) Avogadro s Number: 6.02x10 23 Standard Pressure and Temp 273K 1.00 atm (101.3kPa) 1 st Law of Thermodynamics U internal energy W work done by thermal system Q heat flow into thermal system 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 Conversions 1 cal = 4.186 J 1 L = 1000 cm 3 1 m 3 = 1000 L Isothermal (constant temp) Adiabatic ( Q = 0) Efficiency General Otto Cycle r compression ratio Carnot Cycle Entropy Ideal Gas Thermal Resistance Thermal Resistance, Series Thermal Resistance, Parallel Refrigerators General K coefficient of performance H heat current P power input Carnot Water Properties c = 1 cal/(g- C) = 4.186J/(g- C) L f = 79.6 cal/g L v = 540 cal/g ρ = 1 g/cm 3 = 1 kg/l = 1000 kg/m 3 = 62.4 lb/ft 3 L f = Latent heat of fusion L v = Latent heat of vaporization 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 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
EF 152 Final Exam, Fall, 2011 Page 5 of 10 EF 152 Final Exam, Fall, 2011 Page 6 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) 6. (6 pts) A copper weight is placed on top of a 0.5 kg block of wood floating in water. What is the mass of the copper if the top of the wood block is exactly at the water s surface? =0.6 10 kg/m, =8.9 10 kg/m 1. (1 pt) Consider two identical pails of water filled to the brim. One pail contains only water, the other has a piece of wood floating in it. Which pail has the greater weight? a. pail with water only b. pail with wood c. they both weigh the same A 2. (1 pt) Consider a wave on a string moving to the right. What is the direction of the velocity of a particle at the point labeled A? a. b. c. d. e. zero 7. (6 pts) Shane is using a 3.0cm diameter hose to fill his round swimming pool of diameter 6.0m. How long will it take to fill the pool to a depth of 1.2 m if water issues from the hose at a speed of 0.40 m/s? 3. (1 pt) A gas is maintained at a constant temperature while the pressure is doubled. The internal energy: a. is reduced by a factor of 2 b. does not change c. is increased by a factor of 2 d. is increased by a factor of 4 4. (1 pt) Two charged particles are 3 m apart and the force between them is -4x10-6 N. Determine the factor by which the force between the charged particles changes if they are 1 m apart. a. 1/9 b. 1/3 c. 3 d. 9 5. (6 pts) Isaac, 220 lb, is painting a barn for his camel. The ladder, 20 lb, is 6.0 ft from the base of the barn and hits the side of the barn at a height of 8.0 ft. What is the normal force from the wall onto the ladder when Isaac is ⅓ of the way up the ladder? Assume negligible friction on the side of the barn. A separate, complete FBD is required for full credit. 8. (6 pts) On average, the Achilles tendon is 15 cm long and approximately round with a diameter of 8.5 mm. The tendon was found to stretch 3.7 mm under a 13.4 N load. Calculate the modulus of elasticity (E) of this tendon. 8.0 ft 6.0 ft
EF 152 Final Exam, Fall, 2011 Page 7 of 10 9. (6 pts) A police car (Smokey) traveling at 70 mph is chasing the Bandit, whose speedometer is broken. The frequency of Smokey s siren is 912 Hz. The apparent frequency heard by the Bandit is 860 Hz. How fast is he going? Assume the speed of sound in air is 767 mph. EF 152 Final Exam, Fall, 2011 Page 8 of 10 12. (6 pts) A ray of light passes from air (n = 1) into a glass prism at an angle of incidence of 35 o. If the angle of refraction in the glass is 23.7 o, what is the speed of the light in the glass? 10. (6 pts) Two springs of equal length are suspended in parallel. A 2.5 kg weight is added and the system oscillates in simple harmonic motion. If the stiffness of the springs are 12.0 N/m and 7.0 N/m, what is the period of the system? 13. (6 pts) 3 kg of lemonade is initially at 35 C. Determine the amount of ice at 0 C needed to cool the lemonade down to 0 C while melting half the ice. 12 N/m 7 N/m 2.5 kg 11. (6 pts) Larry the Cable Guy is replacing a coaxial cable (copper wire). To determine the length, he sends a longitudinal pulse down the cable and measures the time for it to return. If it takes 0.15 sec for the pulse to return, how long is the cable? E copper = 110 GPa, =8.9 10 kg/m 14. (6 pts) The humble Morrison abode (1200 ft 2 wall area) has insulation with an R value of 2 ft 2 -hr- F/BTU. Determine the R-value of insulation that Shane would need to install in series so that the heat loss is limited to 14000 BTU in 3 hours for a 23 F temperature difference.
EF 152 Final Exam, Fall, 2011 Page 9 of 10 EF 152 Final Exam, Fall, 2011 Page 10 of 10 15. (6 pts) The p-v diagram for the Schleter engine is shown. Determine the amount of work done in one cycle of the Schleter engine. 290 kpa p 18. (6 pts) A 12 V potential is applied across a circuit that has 20μF capacitors. Determine the number of capacitors needed if it is desired to store 8.64x10-3 J of energy in the circuit. 150 kpa V. 0.2 m 3 0.5 m 3 16. (6 pts) Isaac s 400 kg pet camel is at a temperature of 34 C. The specific heat of a camel is 3480 J/kg-K. The camel has an entropy change of 25000 J/K. What is the final temperature of the camel? 19. (6 pts) Determine the current in the, I, in the circuit. I 17. (6 pts) An electron starts from rest at point A where the potential is 12kV. The electron travels 0.76 m to point B where the potential is 18kV. Determine the speed of the electron at point B. 20. (6 pts) A particle with a charge of 8 nc is moving with a velocity of 6 +4 / is moving through a magnetic field of 3 +5 10. What is the force on the particle?