Mock Exam III PH 201, PH 221 April 12, 2015 You will have 1 hour to complete this exam, and must answer 7 of the problems correctly to make a perfect score. 1
Chapter Concept Summary Equations: Cutnell & Johnson Ch 1: sinθ = h O h cosθ = h A h tanθ = h O h A C x = A x + B x C y = A y + B y C 2 = C x 2 + C y 2 Ch 2: Average Speed = v = v 0 + at Distance Elapsed time v = Δ x Δt h 2 = h 2 2 O + h A v = lim Δ x Δt 0 Δt A x = Acosθ a = Δ v Δt A y = Asinθ x x 0 = 1 ( 2 v + v)t = v t + 1 0 0 2 at2 v 2 v 2 0 = 2a( x x 0 ) g = 9.80 m s 2 Graphs: Velocity = slope of graph of position vs. time; Acceleration = slope of graph of velocity vs. time Ch 3: v = r r0 = Δ r t t 0 Δt x component v x = v 0x + a x t x x 0 = v 0x t + 1 2 a x t2 v 2 2 x v 0x = 2a x ( x x 0 ) v v a = 0 t t 0 = Δ v Δt y component v y = v 0y + a y t y y 0 = v 0y t + 1 2 a y t2 v 2 2 y v 0y Projectile motion: a x = 0 a y = -g Ch 4: Newton s 2 nd Law: F net = ma F = ma F x = ma x F y = ma y Equilibrium: F x = F y = 0 = 2a y ( y y 0 ) Gravitational force: Near earth surface: F g = W = mg Farther away: F G = G m 1m 2 r 2 Friction: f max s = µ s F N f k = µf N Conversion factors: Length: 1 inch = 2.54 cm 1 km = 0.6214 mi 1 kg = 1000 g Mass: 1 slug = 14.59 kg 1 kg has weight of 2.205 lb.
Ch 5: Circular motion v = 2πr T a c = v2 r F c = mv2 r Banked curves: tanθ = v2 rg Satellites: v = GM E r Ch 6: Work & Energy W = ( F cosθ)s KE = 1 2 mv2 W = KE f KE 0 Grav. PE: Conservation of mechanical energy: W nc= E f E 0 Power: P = Work Time Ch 7: Impulse & Momentum PE = mgh = Chg.in energy Time Impulse: J = FΔt Momentum: p = mv Impulse-momentum theorem: J = pf p 0 Conserv. of momentum: m 1v f1 vf 2 = m 1v01 v02 m 1 v f1x v f 2x = m 1 v 01x v 02x m 1 v f1y v f 2y = m 1 v 01y v 02y Center of mass: x = m 1x 1 x 2 +... cm m 1 +... v = m 1v 1 v 2 +... cm m 1 +... = Fv Ch 9: Rotational Dynamics (sections.1-.3) Magnitude of torque: τ = F Equilibrium: F x = 0 and F y = 0 τ = 0 Center of gravity: x = W x + W x +... 1 1 2 2 cg W 1 + W 2 +... Ch 10: Simple Harmonic Motion and Elasticity Ideal spring and SHM: F applied x = kx F x = kx Period, frequency: f = 1 T Angular frequency: ω = 2πf Max speed, accel: v max = Aω, a max = Aω 2 ω = k m PE spring = 1 2 kx2 Pendulum: ω = g L Shear: F = S ΔX A Pressure: P=F/A, ΔP = B ΔV L 0 Elastic deformation: F = Y ΔL L 0 A V 0
Ch 11: Fluids Density of substance Mass density: ρ = m/v Specific gravity= Pressure P = F 1000kg m 3 A (Pa or N/m2 ) One atmosphere of pressure: 1.013 x10 5 N/m 2 =760 mm Hg Pressure & depth: P 2 = P 1 +ρgh Pascal s Principle: Any change in pressure applied to a completely-enclosed fluid is transmitted undiminished to all parts of the fluid and the encl;osing walls. Archimedes Principle: The buoyant force is equal to the weight of the fluid that the partially or completely immersed object displaces: F B = W fluid. Mass flow rate = ρav Equation of continuity: ρ 1 A 1 v 1 = ρ 2 A 2 v 2 Continuity for incompressible fluid: A 1 v 1 = A 2 v 2 Q = Av = volume flow rate Bernoulli s equation: P 1 + 1 2 ρv 2 1 + ρgy 1 = P 2 + 1 2 ρv 2 2 + ρgy 2 Force needed to move a layer of viscous fluid with constant speed: F = ηav y Poiseuille s law: Q = πr 4 ( P 2 P 1 ) 8ηL Ch 12: Temperature & Heat T = T C +273.15 Expansion: ΔL = αl 0 ΔT ΔV = βv 0 ΔT Conversion: 1 kcal = 4186 J Specific Heat: Q = mcδt c w = 4186 J/(kg C) Phase change: Q = ml Ch 13: Heat Transfer Conduction: Q t = kaδt L Net radiated power: P net = eσ A T 4 T 0 4 Radiation: Q = eσ T 4 At, σ =5.67 10 8 J / (s m 2 K 4 ) ( ) Ch 14.4: Diffusion. Fick s Law: m = DAΔC ( )t L
PH 201, 221 Problem 1 Water escapes through a small hole in a tank. The center of the circular hole is 1.0 m below the surface of the water, and has a radius of 0.25 m. The tank itself is circular and has a radius of 1.5 m. Compute the velocity of the water leaving the hole. Problem 2 The drawing shows a frictionless incline and pulley system. The two blocks are connected by a wire (the mass per unit length of the wire is 0.0275 kg/m) and remain stationary. A transverse wave on the wire has a speed of 71.0 m/s. Find the masses m 1 and m 2 of the blocks. Problem 3 A cowboy fires a silver bullet with a muzzle speed of 200 m/s into the pine wall of a saloon. Assume all the internal energy generated by the impact remains with the bullet. What is the temperature change of the bullet? The specific heat of silver is 234 J/(kg o C). Problem 4 Assume a certain liquid, with density 1230 kg/m 3, exerts no friction force on spherical objects. A ball of mass 2.10 kg and radius 9.00 cm is dropped from rest into a deep tank of this liquid from a height of 3.30 m above the surface. 1. Calculate how deep the ball submerges into the liquid. 2. With what speed does the ball pop up out of the liquid? Problem 5 A poorly designed electronic device has two bolts attached to different parts of the device that almost touch each other in its interior as shown. The steel and brass bolts are at different electric potentials, and if they touch, a short circuit will develop, damaging the device. The initial gap between the ends of the bolts is 5.0 µm at 27 o C. The length of the steel bolt is 0.010 m and the length of the brass bolt is 0.030 m. At what temperature will the bolts touch? The coefficient of linear expansion for brass is 19 10 6 ( o C) 1 and is 11 10 6 ( o C) 1 for steel. 7
PH 201, 221 Problem 6 Students in a physics lab are to determine the specific heat of copper experimentally. They heat 0.150 kg of copper shot to 100 o C and then carefully pour the hot shot into a calorimeter cup containing 0.200 kg of water at 20 o C. The final temperature of the mixture in the cup is measured to be 25 o C. If the aluminum cup has a mass of 0.045 kg, what is the specific heat of copper? Assume that there is no heat loss to the surroundings. Also, the specific heat of water is 4186 J/(kg o C) and the specific heat of aluminum is 920 J/(kg o C). Problem 7 A 470.0 Hz tuning fork is sounded together with an out-of-tune guitar strings, and a beat frequency of 8 Hz is heard. When the string is tightened, the frequency at which it vibrates increases, and the beat frequency is heard to increase. What was the original frequency of the guitar string? Problem 8 The middle C string on a piano is under a tension of 991 N. The period and wavelength of a wave on this string are 3.82 10 3 s and 1.26 m, respectively. Find the linear density of the string. Problem 9 Tsunamis are fast-moving waves generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the Aleutian Islands in Alaska, had a wavelength of 750 km and traveled a distance of 3700 km in 5.8 hr. Compute the speed, frequency, and period of the wave. 8