Physics 212

Test #2 - Sample Test Questions

January 28, 2002

Please explain or show your work for each problem.

  1. A large stone is resting on the bottom of a swimming pool. What is the normal force of the bottom of the pool on the stone equal to?

FN = Weight of stone – The weight of the displaced liquid.

  1. A fountain sends water to a height of 100 m. What must be the pressure (above atmospheric) of the underground water system?

Pbottom = gh = 1000 kg/m3 (9.8 N/kg) (100 m ) = 9.8 x 105 Pa = 9.8 atm

  1. A blimp is filled with 200 m3 of helium. How much mass can the balloon lift? The density of helium is 1/7 that of air, while the density of air is 1/800 that of water. (Ans: 215 kg)

FB

The He balloon is buoyed up by air. Let m be

The mass of balloon and M the mass to be lifted.

FB = mg + Mg

where FB = airVbalimpg mg Mg

M = (air – He )Vbalimp = (1/800 x 1000 kg/m3 – 1/7 x 1/800 x 1000 kg/m3) . 200 m3

M = 214 m3

  1. The water level in a reservoir is maintained at constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface? (Ans: 7.7 m/s)

P1 + ½ v12 + gh1 = P2 + ½ v22 + gh2

P1 + 0 + gh1 = P1 + ½ v22 + 

v2 = v2 =

Please explain or show your work clearly for each of the following questions or problems.

  1. A boat is loaded with wood floats in a swimming pool. When the wood is thrown overboard, what will happen to the swimming pool level.

The water level will stay the same. This is because an object floating will displace fluid as much as its weight, but an object submerged or sinking will displace fluid as much as its volume. Whether the wood is on boat or on water, still floats.

  1. A scale from which a rock is suspended reads 5.0 N when the rock is out of water and 3.0 N when the rock is submerged. What is the density of the rock?

Wair - Wwater = Buoyancy force =wVobj g

kg/m3 .Vobj (9.8 N/kg)

Vobj = 2.04 x 10-4 m3

obj = m /Vobj

obj = obj = 2500 kg/m3

  1. The siphon shown is used to transfer water from a higher level to a lower level. If the fluid is drawn up and is continuous through the tube, determine the velocity of flow of gasoline if the vertical distance from the liquid surface to the outlet is 1.0 m?

Given: P1 = P2 = Atmospheric pressure, v1 = 0 , h1=0, h2 = -1 m

Using Bernoulli’s Equation:

P1 + ½ v12 + gh1 = P2 + ½ v22 + gh2

With point 1 taken at where water inters the siphon and point 2 is when it leaves the siphon. Also the reference level for height measurement is taken at the reservoir water level.

P1 + 0 + 0 = P2 + ½ v22 +  (9.8 m/s2) (–1.0 m)

v2 = v2 = 4.43 m/s

  1. Assume a wave is traveling on a light string toward a heavy string which is attached to it. Compare the phases of the reflected and transmitted waves. Sketch a wave diagram.

The wave is reflected at the boundary heavy string with 180 degrees out of phase with the original wave. The wave is transmitted to the heavy string without phase shift. (see diagram)

  1. A vertical spring stretches by 0.050 m when a 0.10 kg mass is attached to it. The spring is then displaced 0.20m below the new equilibrium position and released. Determine (a) the force constant of the spring and (b) period of the motion.

Given: x = 0.050m , m = 0.10 kg , A = 0.20 m

Find : k = ? and T = ?

(a)F = kx k =

(b) T = 0.449s

  1. A frequency of 120 Hz produces a third harmonic standing wave in a string 1.0 m long. The mass of the string is 5.0 x 10-4 kg. (a) Draw an accurate diagram and determine the wavelength of the wave producing the standing wave. Determine (b) the velocity of the waves and (c) tension in the string.

Given: f3 = 120 Hz , n = 3 , L = 1.0 m , m = 5 x 10-4 kg

Find : v = ? , T = ?

(a)

(b)v = f3 where from diagram 3/2 = L or  = 0.667m

v = 0.667 m . 120 Hz v = 80 m/s

(c)

T = 3.2 N

  1. What are the behavior of all waves?

a) Reflectionb) Refractionc) diffractiond) Interference

  1. What is the phase change when a traveling wave is reflected by a more dense medium?

The reflected wave wave will have 180 degree phase change.

  1. A wave described by y = 0.15 sin [/16 (2x – 64t)]. At time zero a snapshot is taken of the wave. For what values of x does the maximum displacement occur?

Maximum displacement occurs when sin [/16 (2x – 64t)] = /2

Or when x = 4 m

  1. The lowest A on a piano has a frequency of 27.5 Hz. If the tension in a 2-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire? (Ans: 50 grams)

where ½ 1 = L  =

 = 0.051 Kg = 51 g

  1. If y = 0.02 sin (30x – 400t) (SI units), what is the frequency and the wave number of the wave?
  1. A horn of an automobile blows with a frequency of 1000 Hz as it passes you. If the car is moving at a speed of 80 m/s relative to you, what is the variation in frequency?
  1. Approximately how many times faster is the speed of sound under water than in air? ( the bulk modulus of water is 2.1 x 109 N/m2)
  1. A bat flying at 5 m/s, emits a chirp at 40 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat? (vsound = 340 m/s)
  1. If the tension in a guitar is increased by a factor of three, by what factor is the fundamental frequency at which the string vibrates changed?
  1. Two loudspeakers are placed next to each other and driven by the same source at 500 Hz. A listener is positioned in front of the two speakers and on the line separating them, thus creating a constructive interference at the listener’s ear. What minimum distance would one of the speakers be moved back away form the listener to produce destructive interference at the listener’s ear? (vsound = 340 m/s)
  1. A fundamental standing wave is produced in a taut string of a violin. If the string is tuned up by creating more tension in the string, what happens to the wavelength of the sound produced?
  1. The fundamental frequency of an organ pipe which is open at both ends corresponds to a middle C (261.6 Hz). What is the length of the pipe? (Ans:65.7cm)
  1. Two harmonic waves are described by

y1 = 4 sin (x + 3t)

y2 = 4 sin (x – 3t)

What is the maximum amplitude at x = 47 cm? (Ans: 8 cm)

  1. A stretched string is observed to vibrate in three equal segments when driven by a 480 Hz oscillator. What is the natural frequency of vibration for this string?
  1. Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin(x) cos (3t) where x is in meters and t in seconds. What is the distance (in meters) between first two antinodes? (Ans: 1.0 m)