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.
2. 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
3. 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
F  mg
where FB = airVbalimpg
mg Mg
M B
g
M = (air – He )Vbalimp = (1/800 x 1000 kg/m3 – 1/7 x 1/800 x 1000 kg/m3) . 200 m3
M = 214 m3
4. 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 =
2gh1
v2 =
2(9.8m / s 2 )(3.0)  7.7m / s
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.
2. 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
5N
9.8 N / kg
obj =
obj = 2500 kg/m3
-4
3
2.04 x 10 m
3. 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 = 2(9.8 sm2 )(1.0m)
v2 = 4.43 m/s
4. 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)
5. 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
Find : k = ? and T = ?
(a)
F = kx
(b)
T  2
k=
m
 2
k
,
A = 0.20 m
m
mg 0.10kg9.8 s 2
kg

 19.6 2
x
0.050m
s
0.10kg
kg
19.6 2
s
T = 0.449s
6. 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)
(c)
v = f3 where from diagram 3/2 = L or  = 0.667m
v = 0.667 m . 120 Hz
v = 80 m/s
v
T

T = 3.2 N
T  v 2 
m 2 5 x10 4 kg
v 
(80m / s) 2
L
1.0m
7. What are the behavior of all waves?
a) Reflection b) Refraction c) diffraction d) Interference
5. 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.
6. 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
7. 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)
v
T

 1 f 1 where ½ 1 = L
=
T
f 1 (2 L) 2
2
 = 0.051 Kg = 51 g
8.
If y = 0.02 sin (30x – 400t) (SI units), what is the frequency and the wave number
of the wave?
9. 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?
10. 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)
11. 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)



12. 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?
13. 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)
14. 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?
15. 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)
16. 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)
17. 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?
18. 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)