Transcript Physics 131: Lecture 14 Notes

Physics 151
Lecture 27-36 / Chapters 13-16 / HW 10-13
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Review of Concepts
Example Exam-III
Problems from CHAPTER :
#13 / Gravity, Kepler’s laws
#14 / fluid statics and dynamics
#15 / Simple Harmonic Motion
#16 / Waves
Physics 151: Lecture 21, Pg 1
Example Exam-III:
Problem 1.a

Suppose you know the length (L) and the total mass of
the bob (M) plus the string (m) of the simple pendulum.
You than calculate the period of this pendulum assuming
the total mass (M+m) is all concentrated in the bob, as
we often do. Is this calculated period:
(A) lower

(B) the same
(C) higher
than the period of the real pendulum ?
m
L
M
Physics 151: Lecture 21, Pg 2
Example Exam-III:
Problem 1.b

A satellite is in orbit about the earth at a distance of
0.5RE above the earth’s surface. To change orbit it
fires its booster rockets to double its height above the
Earth’s surface. By what factor did its speed change
(v2/v1) ?
(A) 4/3
(B) 3/4
(C) (3/4)1/2
(D) (4/3)1/2
v1
v2
RE
Physics 151: Lecture 21, Pg 3
Example Exam-III:
Problem 1.c
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An air stream moves from left to right through a tube
that is constricted at the middle. Three Ping-Pong
balls are levitated by the air escaping though three
vertical columns as shown. When the balls are in
equilibrium what are their relative heights? Explain.
(A) h1 = h2 = h3
(B) h1 = h3 > h2
1
(C) h1 = h3 < h2
2
3
h1
(D) h1 < h3 < h2
air
air
air
air
air
Physics 151: Lecture 21, Pg 4
Example Exam-III:
Problem 2.

The equation: y(x,t) = (2/p) cos [p( x – 4 t)] gives
the particle displacement of a string in which a
simple harmonic wave is propagating (all units
are SI). The string is under tension of 10 N.

a) What is the speed of that wave ?

b) At t = 2s what is the velocity of the string at
x = 10 m ?
Physics 151: Lecture 21, Pg 5
Example Exam-III:
Problem 3

A U-tube is open on both sides to the atmosphere is
partially filled with mercury. Water is then poured
into both arms. If the equilibrium configuration of the
tube is as shown in the Figure, with h2 = 1.00 cm and
the diameters of the left arm of U-tube is d = 2.00
cm. Determine the value of the h1.
d
r(mercury) = 13.6 g/cm3
r(water) = 1.0 g/cm3
2d
h1
water
water
h2
mercury
Physics 151: Lecture 21, Pg 6
GRAVITY: Example
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Which of the following quantities is conserved for
a planet orbiting a star in a circular orbit? Only
the planet itself is to be taken as the system; the
star is not included.
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a.
b.
c.
d.
e.
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Momentum and energy.
Energy and angular momentum.
Momentum and angular momentum.
Momentum, angular momentum and energy.
None of the above.
Physics 151: Lecture 21, Pg 7
Example

A satellite is in a circular orbit about the Earth at an
altitude at which air resistance is negligible. Which
of the following statements is true?
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a. There is only one force acting on the satellite.
b. There are two forces acting on the satellite,
and their resultant is zero.
c. There are two forces acting on the satellite,
and their resultant is not zero.
d. There are three forces acting on the satellite.
e. None of the preceding statements are correct.
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Physics 151: Lecture 21, Pg 8
Example
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A satellite is placed in a geosynchronous orbit. In this
equatorial orbit with a period of 24 hours, the satellite
hovers over one point on the equator. Which statement
is true for a satellite in such an orbit ?
a. There is no gravitational force on the satellite.
b. There is no acceleration toward the center of the Earth.
c. The satellite is in a state of free fall toward the Earth.
d. There is a tangential force that helps the satellite keep
up with the rotation of the Earth.
e. The force toward the center of the Earth is balanced by
a force away from the center of the Earth.
Physics 151: Lecture 21, Pg 9
Example
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A projectile is launched from the surface of a planet
(mass = M, radius = R). What minimum launch
speed is required if the projectile is to rise to a
height of 2R above the surface of the planet?
Disregard any dissipative effects of the
atmosphere.
Physics 151: Lecture 21, Pg 10
Example
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A satellite circles planet Roton every 2.8 h in an
orbit having a radius of 1.2x107 m. If the radius of
Roton is 5.0x106 m, what is the magnitude of the
free-fall acceleration on the surface of Roton?

a.
b.
c.
d.
e.
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31 m/s2
27 m/s2
34 m/s2
40 m/s2
19 m/s2
Physics 151: Lecture 21, Pg 11
FLUIDS:
Example
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Figure on the right shows
Superman attempting to drink
water through a very long
straw. With his great strength
he achieves maximum possible
suction. The walls of the
tubular straw do not collapse.

(a) Find the maximum height
through which he can lift the
water.
Physics 151: Lecture 21, Pg 12
Lecture 29, ACT 2b
Hydraulics
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Consider the systems shown to the
right.
In each case, a block of mass M
is placed on the piston of the large
cylinder, resulting in a difference dI
in the liquid levels.
If A10 = 2A20, compare dA and dC.
dA
A1
A10
dC
A1
A) dA = (1/2)dC
B) dA = dC
M
M
A20
C) dA = 2dC
Physics 151: Lecture 21, Pg 13
Lecture 29, ACT 3
Buoyancy
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A lead weight is fastened to a large
styrofoam block and the
combination floats on water with
the water level with the top of the
styrofoam block as shown.
If you turn the styrofoam+Pb
upside down, what happens?
A) It sinks
B)
styrofoam
Pb
C)
styrofoam
Pb
Pb
styrofoam
D)
styrofoam
Pb
Physics 151: Lecture 21, Pg 14
Example
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A tank containing a liquid
of density r has a hole in its
side at a distance h below
the surface of the liquid.
The hole is open to the
atmosphere and its
diameter is much smaller
than the diameter of the
tank.
What is the speed with of
the liquid as it leaves the
tank.
h
r
v=?
Physics 151: Lecture 21, Pg 15
Venturi Meter
v=?
Can we know
what is v from
what we can
measure ?
h
A1, A2
rHg
rair
Physics 151: Lecture 21, Pg 16
Example

Figure on the right shows a
stream of water in steady flow
from a kitchen faucet. At the
faucet the diameter of the
stream is 0.960 cm. The
stream fills a 125-cm3
container in 16.3 s. Find the
diameter of the stream 13.0 cm
below the opening of the
faucet.
d = 0.247 cm
Physics 151: Lecture 21, Pg 17
Simple Harmonic Motion
Lecture 31, Act 3
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You are sitting on a swing. A friend gives you a
small push and you start swinging back & forth
with period T1.
Suppose you were standing on the swing rather
than sitting. When given a small push you start
swinging back & forth with period T2.
Which of the following is true:
(a) T1 = T2
(b) T1 > T2
(c) T1 < T2
Physics 151: Lecture 21, Pg 18
Lecture 31, Act 4
Simple Harmonic Motion
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a)
b)
c)
d)
e)
Two clocks with basic timekeeping mechanism
consist of
1) a mass on a string and 2) a simple pendulum.
Both have a period of 1s on Earth. When taken to
the moon which one of the statements below is
correct ?
the periods of both is unchanged.
one of them has a period shorter than 1 s.
the pendulum has a period longer than 1 s.
the mass-spring system has a period longer than 1s.
both c) and d) are true.
Physics 151: Lecture 21, Pg 19
Lecture 31, Act 4
Period
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What length do we make the simple pendulum so that it
has the same period as the rod pendulum?
LS
3
(a) LS  LR
2
(b)
LR
2
LS  LR
3
(c) LS  LR
Physics 151: Lecture 21, Pg 20
Lecture 33, Act 1
Resonant Motion
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Consider the following set of pendula all attached to the
same string
A
D
B
If I start bob D swinging which of the
others will have the largest swing amplitude ?
(A)
(B)
C
(C)
Physics 151: Lecture 21, Pg 21
WAVES: Example
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The figure on the right shows a sine
wave on a string at one instant of time.
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Which of the graphs on the
right shows a wave where
the frequency and wave
velocity are both doubled ?
Physics 151: Lecture 21, Pg 22
Example
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Write the equation of a wave, traveling along the
+x axis with an amplitude of 0.02 m, a frequency
of 440 Hz, and a speed of 330 m/sec.
A.
b.
c.
d.
e.
y = 0.02 sin [880p (x/330 – t)]
y = 0.02 cos [880p x/330 – 440t]
y = 0.02 sin [880p(x/330 + t)]
y = 0.02 sin [2p(x/330 + 440t)]
y = 0.02 cos [2p(x/330 - 440t)]
Physics 151: Lecture 21, Pg 23
Example
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For the transverse wave described by
y = 0.15 sin [ p(2x - 64 t)/16] (in SI units),
determine the maximum transverse speed of
the particles of the medium.
a.
b.
c.
d.
e.
0.192 m/s
0.6p m/s
9.6 m/s
4 m/s
2 m/s
Physics 151: Lecture 21, Pg 24
Lecture 35, Act 2
Wave Power

A wave propagates on a string. If both the amplitude
and the wavelength are doubled, by what factor will
the average power carried by the wave change ?
i.e. Pfinal/Pinit = X
(a) 1/4
(b) 1/2
(c) 1
(d) 2
(e) 4
initial
final
Physics 151: Lecture 21, Pg 25
Lecture 35, Act 4
Traveling Waves
Two ropes are spliced
together as shown.
A short time after the
incident pulse shown in
the diagram reaches the
splice, the ropes
appearance will be that in
• Can you determine the relative amplitudes of the
transmitted and reflected waves ?
Physics 151: Lecture 21, Pg 26
Additional Simple Problems
Physics 151: Lecture 21, Pg 27
GRAVITY:
Force and acceleration
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Suppose you are standing on a bathroom scale in
Physics 203 and it says that your weight is W. What
will the same scale say your weight is on the surface
of the mysterious Planet X ?
You are told that RX ~ 20 REarth and MX ~ 300 MEarth.
(a)
0.75 W
(b)
1.5 W
(c)
2.25 W
X
E
Physics 151: Lecture 21, Pg 28
Lecture 28, Act 2
Satellite Energies

A satellite is in orbit about the earth a distance of
0.5R above the earth’s surface. To change orbit it
fires its booster rockets to double its height above the
Earth’s surface. By what factor did its total energy
change ?
(a)
(b)
(c)
(d)
(e)
1/2
3/4
4/3
3/2
2
Physics 151: Lecture 21, Pg 29
Example
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The figure below shows a planet traveling in a
clockwise direction on an elliptical path around a
star located at one focus of the ellipse. When the
planet is at point A,

a.
b.
c.
d.
e.
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its speed is constant.
its speed is increasing.
its speed is decreasing.
its speed is a maximum.
its speed is a maximum.
Animation
Physics 151: Lecture 21, Pg 30
Example
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A spacecraft (mass = m) orbits a planet (mass =
M) in a circular orbit (radius = R). What is the
minimum energy required to send this spacecraft
to a distant point in space where the gravitational
force on the spacecraft by the planet is
negligible?
a. GmM/(4R)
b. GmM/R
c. GmM/(2R)
d. GmM/(3R)
e. 2GmM/(5R)
Physics 151: Lecture 21, Pg 31
See text: 14.4
ACT 3-B
Even More Fun With Buoyancy

A plastic ball floats in a cup of water with
half of its volume submerged. Next some
oil (roil < rball < rwater) is slowly added to
the container until it just covers the ball.
water

Relative to the water level, the ball
will:
(A) move up
(B) move down
(C) stay in same place
Physics 151: Lecture 21, Pg 32
Lecture 29, ACT 2a
Hydraulics

Consider the systems shown to the
right.
In each case, a block of mass M
is placed on the piston of the large
cylinder, resulting in a difference dI
in the liquid levels.
If A2 = 2A1, compare dA and dB.
A) dA=(1/2)dB
B) dA = dB
dA
A1
M
A10
dB
A2
M
A10
C) dA = 2dB
Physics 151: Lecture 21, Pg 33
Example

Water is forced out of a fire extinguisher by air
pressure, as shown in Figure below. How much
gauge air pressure in the tank (above
atmospheric) is required for the water jet to have
a speed of 30.0 m/s when the water level in the
tank is 0.500 m below the nozzle?
Physics 151: Lecture 21, Pg 34
Lecture 32, Act 3
Period

All of the following pedulum bobs have the same
mass. Which pendulum rotates the fastest, i.e.
has the smallest period? (The wires are identical)
R
R
R
R
A)
B)
C)
D)
Physics 151: Lecture 21, Pg 35
Lecture 34, Act 1
Wave Motion


The speed of sound in air is a bit over 300 m/s, and
the speed of light in air is about 300,000,000 m/s.
Suppose we make a sound wave and a light wave
that both have a wavelength of 3 meters.
What is the ratio of the frequency of the light wave
to that of the sound wave ?
(a) About 1,000,000
(b) About .000,001
(c) About 1000
Physics 151: Lecture 21, Pg 36
Example

Bats can detect small objects such as insects
that are of a size on the order of a wavelength. If
bats emit a chirp at a frequency of 60 kHz and
the speed of soundwaves in air is 330 m/s, what
is the smallest size insect they can detect ?
a.
b.
c.
d.
e.
f.
1.5 cm
5.5 cm
1.5 mm
5.5 mm
1.5 um
5.5 um
Physics 151: Lecture 21, Pg 37
Lecture 34, Act 2
Wave Motion


A harmonic wave moving in the positive x direction
can be described by the equation
y(x,t) = A cos ( kx - wt )
Which of the following equation describes a harmonic
wave moving in the negative x direction ?
(a) y(x,t) = A sin ( kx - wt )
(b) y(x,t) = A cos ( kx + wt )
(c) y(x,t) = A cos (-kx + wt )
Physics 151: Lecture 21, Pg 38
Lecture 34, Act 4
Wave Motion


A heavy rope hangs from the ceiling, and a small
amplitude transverse wave is started by jiggling the
rope at the bottom.
As the wave travels up the rope, its speed will:
v
(a) increase
(b) decrease
(c) stay the same

Can you calcuate how long will it take for a pulse
travels a rope of length L and mass m ?
Physics 151: Lecture 21, Pg 39