Final Mock Exam PH 201-1C

Transcription

1 Final Mock Exam PH 201-1C April 18, 2015 You will have 2 hours to complete this exam. You must answer 15 questions to make a perfect score of

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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 201-1C 1. Our system consists of a frictionless incline and pulley system, inclined at 31 o. 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 mass of the hanging block. 2. 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. Calculate how deep the ball submerges into the liquid. 3. Two motorcycles are traveling due east with different velocities. However, four seconds later, they have the same velocity. During this four-second interval, cycle A has an average acceleration of 2.3 m/s 2 due east, while cycle B has an average acceleration of 4.1 m/s 2 due east. By how much did the speeds differ at the beginning of the four-second interval? 4. A golfer hits a shot to a green that is elevated 3 m above the point where the ball is struck. The ball leaves the club at a speed of 16.3 m/s at an angle of 38.1 o above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands. 5. A hot-air balloon is rising straight up with a speed of 2 m/s. A ballast bag is released from rest relative to the balloon at 11.4 m above the ground. How much time elapses before the ballast bag hits the ground? 6. At an instant when a soccer ball is in contact with the foot of a player kicking it, the horizontal or x component of the ball s acceleration is 795 m/s 2 and the vertical or y component of its acceleration is 1060 m/s 2. The ball s mass is 0.41 kg. What is the magnitude of the net force acting on the soccer ball at this instant? 7. Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The mass of the man is 97 kg, and the mass of the woman is 49 kg. The woman pushes on the man with a force of 54 N due east. Determine the acceleration (magnitude and direction) of the man and woman. 8. A Mercedes-Benz 300SL (m = 1500 kg) is parked on a road that rises 10 o above the horizontal. Calculate the static frictional force that the ground exerts on the tires. 9. The aorta is a major artery, rising upward from the left ventricle of the heart and curving down to carry blood to the abdomen and lower half of the body. The curved artery can be approximated as a semicircular arch whose diameter is 4.4 cm. If blood flows through the aortic arch at a speed of 0.45 m/s, what is the magnitude (in m/s 2 ) of the blood s centripetal acceleration? 10. A penny is placed at the outer edge of a disk (radius = m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.50 s. Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. 7

8 PH 201-1C 11. A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r = 16.0 m, how fast is the roller coaster traveling at the bottom of the dip? 12. A golf club strikes a kg golf ball in order to launch it from the tee. For simplicity, assume that the average net force applied to the ball acts parallel to the ball s motion, has a magnitude of 6750 N, and is in contact with the ball for a distance of m. With what speed does the ball leave the club? 13. The hammer throw is a track-and-field event in which a 7.2 kg ball (the hammer ), starting from rest, is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 27.0 m/s. For comparison, a.22 caliber bullet has a mass of 2.6 g and, starting from rest, exits the barrel of a gun with a speed of 402 m/s. Determine the work done to launch the motion of both the hammer and the bullet. 14. 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? 15. A spring stretches by m when a 2.0 kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f = 2.6 Hz? 16. 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. 17. What is the smallest number of whole logs (ρ = 745kg/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? 18. 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. 19. At a distance of 3.8 m from a siren, the sound intensity is W/m 2. Assuming that the siren radiates sound uniformly in all directions, find the total power radiated. 8

9 PH 201-1C 20. A piccolo and a flute can be approximated as cylindrical tubes with both ends open. The lowest fundamental frequency produced by one kind of piccolo is Hz, and that produced by one kind of flute is Hz. What is the ratio of the piccolo s length to the flute s length? 21. Two ultrasonic sound waves combine and form a beat frequency that is in the range of human hearing for a healthy young person. The frequency of one of the ultrasonic waves is 83 khz. (The range of hearing for a healthy young person is 20 Hz to 20 khz.) What is the smallest possible value for the frequency of the other ultrasonic wave? What is the largest possible value for the frequency of the other ultrasonic wave? 9