# PH202 Recitation Week 10 Problem Set Winter 2015

## Transcription

PH202 Recitation Week 10 Problem Set Winter 2015

PH202 Recitation Week 10 Problem Set Winter 2015 Ryan Scheirer Email: [email protected] My Website: http://people.oregonstate.edu/~scheirer/PH202_REC.html Problem 01 Consider a hard drive platter of a computer, a circular disk of diameter d = 3.5inches, that rotates at a constant 7200RP M . (a) What is the angular velocity of the platter? (b) If the reading head of the hard drive is located at the outer most part of the platter, what is the linear speed of a point on the platter just below it? (c) If a single bit requires 0.50µm of length along the direction of motion, how many bits per second can the writing head write when it is at the outer most part of the platter? (d)How many bits per second can the writing head write when it is 2.54cm from the axis of rotation? Problem 02 A small wheel of radius r1 = 8cm is used to drive a larger wheel of radius r2 = 14cm as shown in the figure for 12.2 seconds. below. The small wheel increases its angular speed from rest at a uniform rate of 1.5 rad s2 For the next 10 seconds the angular acceleration is zero. Finally, the angular acceleration of the larger . (Assume the wheels never slip with respect to each other). (a) Find the final rotational wheel is 1.0 rad s2 speed of both wheels at the end of the initial 12.2 seconds. (b) Plot a graph of angular frequency vs time for both wheels for a duration of 40 seconds. (c) If a fire fly was located on the outermost part of the smaller wheel, and a lady bug on the outermost part of the larger wheel, what total distance did the firefly travel after 40 seconds? (d) Compare this distance to the distance the lady bug traveled. 1 Problem 03 A truss is made by hanging two uniform rafters of mass m = 15.3kg as shown in the figure below. They rest on an essentially frictionless floor and are held together by a rope. A mass M = 51kg is hung from their apex. Find the tension in the rope. Problem 04 The Achilles tendon is attached to the rear of the foot as shown in the figure below. When a person elevates himself just barely off the floor on the ”ball of one foot”, estimate the tension in the Achilles tendon (pulling upward), and the downward force exerted by the lower leg bone on the foot. Assume the person has a mass of 72kg and D is twice as long as d. Problem 05 A vacuum pump is used to remove all the air from a glass jar. Can you determine the temperature of a vacuum created inside the jar? 2 Problem 06 Explain why burns caused by steam at 100◦ C on the skin are often more severe than burns caused by water at 100◦ C. Problem 07 Can the temperature of a system remain constant even though heat flows into or out of it? If so, give examples. Problem 08 A gas is allowed to expand (a) isothermally, (b) adiabatically. Does the entropy increase decrease, or stay the same? Problem 09 Which is possible: converting (i) 100 J of work entirely into 100 J of heat, (ii) 100 J of heat entirely into 100 J of work? (a) Only (i) is possible. (b) Only (ii) is possible. (c) Both (i) and (ii) are possible. (d) Neither (i) nor (ii) is possible. Problem 10 Refer to the figure below. Both beakers contain water. Which beaker weights more? 3 Problem 11 You hold a piece of wood in one hand and a piece of iron in the other. Both pieces have the same volume, and you hold them fully underwater at the same depth. At the moment you let go of them, which one experiences the greater buoyancy force? (a) The piece of wood. (b) The piece of iron. (c) They experience the same buoyancy force. (d) More information is needed. Problem 12 While snooping around Dr. No’s secrete island, Crab Key, you get spotted by Dr. No’s guards. In order to evade them, you use bamboo stalks to breathe underwater while they pass by. If the maximum pressure difference your lungs can manage and still breathe is 11300P a, what would be the deepest you could go and still breathe? Problem 13 Water and oil are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in the figure below. What is the density of the oil? Problem 14 A fire hose exerts a force on the person holding it. This is because the water accelerates as it goes from the hose through the nozzle. How much force is required to hold a 7.0-cm-diameter hose delivering through a 0.75-cm-diameter nozzle? 420 L/min Problem 15 The displacement from equilibrium of a 1 kg mass attached to a spring is described by the equation. 3 x(t) = cos(4π t) (1) 2 (a) What is the period, (b) spring constant, (c) maximum speed, (d) total mechanical energy of this motion, and (e) velocity at t = 0.33seconds. 4 Problem 16 A spring is attached to a ceiling, with a mass hanging from it as shown in figure (a) below. It is then stretched a distance A and allowed to undergo simple harmonic motion. Now consider stretching the mass a distance 2A. What happens to the (a) energy of the system, (b) the maximum velocity, (c) the maximum acceleration of the mass? Problem 17 Which of the following represent a simple harmonic oscillator? (a) F = −2.3y (b) F = 8.6x (c) F = −4θ (d) F = − 12 x2 Problem 18 A 2.2 kg mass oscillates on a spring with a force constant of 250 N . The period is measured to be 0.615 m seconds. Is this system a damped harmonic oscillator? 5 Problem 19 When you drive your car over a bump, the springs connecting the wheels to the car compress. Your shock absorbers then damp the subsequent oscillation, keeping your car from bouncing up and down on the springs. The figure below shows real data for a car driven over a bump. Estimate the frequency and the time constant for this damped oscillation. Problem 20 A string of mass 0.65kg is stretched between two supports 28m apart. (a) If the tension in the string is 150N , how long will it take a pulse to travel from one support to the other? (b) What would the tension in the string have to be if you wish to cut the time it takes a pulse to reach the other support in half ? Problem 21 A tsunami is a sort of pulse or wave packet consisting of several crests and troughs that become dramatically large as they enter shallow water at the shore. Suppose a tsunami of wavelength 235 km and velocity 550km/hr travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.) Problem 22 A single mosquito 5.0 m from a Barn owl makes a sound approximately equal to the threshold of human hearing. It is been observed that threshold sound intensity level of Barn Owls can be as low as −20dB. What is the furthest distance a single mosquito can be such that a Barn Owl can still hear it? Problem 23 A bat at rest sends out ultrasonic sound waves at 50kHz and receives them returned from an object moving directly away from it at 25m/s. What is the received sound frequency the bat hears? 6 Problem 24 A speaker in an open field emits a constant source of sound at 392Hz. The velocity of the wind that day is 8m/s from the north. Four observers at rest are located at locations (i) due north, (ii) due south (iii) due east, and (iv) due west. of the speaker. (a) What frequencies will each of these observers hear? Now consider a two cyclist, one heading north and the other west, both at 10m/s towards the speaker. (b) What frequency is heard by each of the cyclist? Problem 25 Two identical loudspeakers separated by a distance d emit 170 Hz sound waves along the x-axis. As you walk along the axis, away from the speakers, you don’t hear anything even though both speakers are on. What are some possible values for d? Problem 26 You are standing 2.50 m directly in front of one of the two loudspeakers shown in the figure below. They are 3.00 m apart and both are playing a 686 Hz tone in phase. As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? Problem 27 Two loudspeakers are placed 3.00 m apart, as shown in the figure below. They emit 474-Hz sounds, in phase. A microphone is placed 3.20 m distant from a point midway between the two speakers, where an intensity maximum is recorded. (a)How far must the microphone be moved to the right to find the first intensity minimum? 7 8