Final Mock Exam PH 221-1D
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1 Final Mock Exam PH 221-1D April 18, 2015 You will have 2 hours to complete this exam. You must answer 8 questions to make a perfect score of 80. 1
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4 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 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 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 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 = mi 1 kg = 1000 g Mass: 1 slug = kg 1 kg has weight of lb.
5 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 cm m v = m 1v 1 v cm m = 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 cg W 1 + W 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
6 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: 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 ρv ρgy 1 = P ρv 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 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 = J / (s m 2 K 4 ) ( ) Ch 14.4: Diffusion. Fick s Law: m = DAΔC ( )t L
7 PH 221-1D 1. 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 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 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. (a) Calculate how deep the ball descends into the liquid. (b) Calculate the speed at which the ball leaves the liquid. 3. A poorly designed electronic device has two bolts attached to different parts of the device that almost touch each other in its interior. 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 m and the length of the brass bolt is m. At what temperature will the bolts touch? The coefficient of linear expansion for brass is ( o C) 1 and is ( o C) 1 for steel. 4. You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professors head, where should the professor be when you drop the egg? Ignore air resistance. 5. Two blocks having masses m 1 = 10 kg and m 2 = 15 kg are connected by a string passing over a pulley. The pulley has a mass of 15 kg and a radius of 0.5 m. The system is initially at rest. What is the speed of block 2 after it has descended 3 m? At the same time, what is the angular speed of the pulley? 6. What is the smallest number of whole logs (ρ = 745 kg/m 3, radius = m, length = 2.79 m) that can be used to build a raft that will carry four people, each of whom has a mass of 74.5 kg? 7. Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree trunk at an angle of 26.3 o above the horizontal. One child, with a mass of 44.4 kg, is hanging 1.31 m along the branch from the tree trunk. The other child, with a mass of 34.8 kg, is hanging 1.97 m from the tree trunk. What is the magnitude of the net torque exerted on the branch by the children? Assume that the axis is located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk. 8. A 250 kg motorcycle is driven around a 12 m tall vertical circular track at a constant speed of 11 m/s. Determine the minimum coefficient of static friction needed to complete the loop. 7
8 PH 221-1D 9. The middle C string on a piano is under a tension of 836 N. The period and wavelength of a wave on this string are s and 1.26 m, respectively. Find the linear density of the string. 10. A 2.50 g bullet, traveling at a speed of 375 m/s, strikes the wooden block of a ballistic pendulum, such as that in the figure below. The block has a mass of 265 g. Find the speed of the bullet/block combination immediately after the collision. How high does the system rise? 8
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