Physics 151 Lecture 27-36 / Chapters 13-16 / HW 10-13

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Physics 151Lecture 27-36 / Chapters 13-16 /
HW 10-13

• Review of Concepts
• Example Exam-III
• Problems from CHAPTER
• 13 / Gravity, Keplers laws
• 14 / fluid statics and dynamics
• 15 / Simple Harmonic Motion
• 16 / Waves

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Example Exam-IIIProblem 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 (Mm) 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 ?

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Example Exam-IIIProblem 1.b

• A satellite is in orbit about the earth at a
  distance of 0.5RE above the earths surface. To
  change orbit it fires its booster rockets to
  double its height above the Earths 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

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Example Exam-IIIProblem 1.c

• 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 gt h2
• (C) h1 h3 lt h2
• (D) h1 lt h3 lt h2

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Example Exam-IIIProblem 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 ?

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Example Exam-IIIProblem 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.
• r(mercury) 13.6 g/cm3
• r(water) 1.0 g/cm3

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GRAVITY Example

• 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.
• a. Momentum and energy.
• b. Energy and angular momentum.
• c. Momentum and angular momentum.
• d. Momentum, angular momentum and energy.
• e. None of the above.

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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?
• 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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Example

• 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.

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Example

• 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.

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Example

• 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. 31 m/s2
• b. 27 m/s2
• c. 34 m/s2
• d. 40 m/s2
• e. 19 m/s2

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FLUIDSExample

• 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.

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Lecture 29, ACT 2bHydraulics

• 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 2A20, compare dA and dC.

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Lecture 29, ACT 3Buoyancy

• 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 styrofoamPb upside down, what
  happens?

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Example

• 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?
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Venturi Meter
v ? Can we know what is v from what we can
measure ? h A1, A2 rHg rair
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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
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Simple Harmonic Motion Lecture 31, Act 3

• 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 gt T2 (c) T1 lt T2
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Lecture 31, Act 4Simple Harmonic Motion

• 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 ?
• a) the periods of both is unchanged.
• b) one of them has a period shorter than 1 s.
• c) the pendulum has a period longer than 1 s.
• d) the mass-spring system has a period longer
  than 1s.
• e) both c) and d) are true.

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Lecture 31, Act 4Period

• What length do we make the simple pendulum so
  that it has the same period as the rod pendulum?

(a) (b) (c)
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Lecture 33, Act 1Resonant Motion

• 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
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WAVES Example

• The figure on the right shows a sine wave on a
  string at one instant of time.

• Which of the graphs on the right shows a wave
  where the frequency and wave velocity are both
  doubled ?

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Example

• 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. y 0.02 sin 880? (x/330 t)
• b. y 0.02 cos 880? x/330 440t
• c. y 0.02 sin 880?(x/330 t)
• d. y 0.02 sin 2?(x/330 440t)
• e. y 0.02 cos 2?(x/330 - 440t)

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Example

• 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. 0.192 m/s
• b. 0.6? m/s
• c. 9.6 m/s
• d. 4 m/s
• e. 2 m/s

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Lecture 35, Act 2Wave 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
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Lecture 35, Act 4Traveling 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 ?

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Additional Simple Problems
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GRAVITYForce and acceleration

• 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
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Lecture 28, Act 2Satellite Energies

• A satellite is in orbit about the earth a
  distance of 0.5R above the earths surface. To
  change orbit it fires its booster rockets to
  double its height above the Earths surface. By
  what factor did its total energy change ?
• (a) 1/2 (b) 3/4 (c) 4/3
• (d) 3/2
• (e) 2

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Example

• 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. its speed is constant.
• b. its speed is increasing.
• c. its speed is decreasing.
• d. its speed is a maximum.
• e. its speed is a maximum.

Animation
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Example

• 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)

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ACT 3-BEven More Fun With Buoyancy
See text 14.4

• A plastic ball floats in a cup of water with half
  of its volume submerged. Next some oil (roil lt
  rball lt rwater) is slowly added to the container
  until it just covers the ball.
• Relative to the water level, the ball will

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Lecture 29, ACT 2aHydraulics

• 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 2A1, compare dA and dB.

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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?

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Lecture 32, Act 3Period

• 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)

C)
B)
A)
D)
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Lecture 34, Act 1Wave 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
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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. 1.5 cm
• b. 5.5 cm
• c. 1.5 mm
• d. 5.5 mm
• e. 1.5 um
• f. 5.5 um

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Lecture 34, Act 2Wave 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 )
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Lecture 34, Act 4Wave 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 ?