2. Physics 151: Lecture 21, Pg 1 Physics 151 Lecture 27-36 / Chapters 13-16 / HW 10-13 l Review of Concepts l Example Exam-III l Problems from CHAPTER : ç#13 / Gravity, Kepler’s laws ç#14 / fluid statics and dynamics ç#15 / Simple Harmonic Motion ç#16 / Waves

3. Physics 151: Lecture 21, Pg 2 Example Exam-III: Problem 1.a l 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 l than the period of the real pendulum ?

4. Physics 151: Lecture 21, Pg 3 Example Exam-III: Problem 1.b l A satellite is in orbit about the earth at a distance of 0.5R E 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 (v 2 /v 1 ) ? (A) 4/3 (B) 3/4 (C) (3/4) 1/2 (D) (4/3) 1/2

5. Physics 151: Lecture 21, Pg 4 Example Exam-III: Problem 1.c l 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. l (A) h1 = h2 = h3 l (B) h1 = h3 > h2 l (C) h1 = h3 < h2 l (D) h1 < h3 < h2

6. Physics 151: Lecture 21, Pg 5 Example Exam-III: Problem 2. The equation: y(x,t) = (2/  ) cos [  ( 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. l a) What is the speed of that wave ? l b) At t = 2s what is the velocity of the string at x = 10 m ?

7. Physics 151: Lecture 21, Pg 6 Example Exam-III: Problem 3 l 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 h 2 = 1.00 cm and the diameters of the left arm of U-tube is d = 2.00 cm. Determine the value of the h 1.  (mercury) = 13.6 g/cm 3  (water) = 1.0 g/cm 3

8. Physics 151: Lecture 21, Pg 7 GRAVITY: Example l 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. l a. Momentum and energy. l b. Energy and angular momentum. l c. Momentum and angular momentum. l d. Momentum, angular momentum and energy. l e. None of the above.

9. Physics 151: Lecture 21, Pg 8 Example l 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? l a. There is only one force acting on the satellite. l b. There are two forces acting on the satellite, and their resultant is zero. l c. There are two forces acting on the satellite, and their resultant is not zero. l d. There are three forces acting on the satellite. l e. None of the preceding statements are correct.

10. Physics 151: Lecture 21, Pg 9 Example l 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.

11. Physics 151: Lecture 21, Pg 10 Example l 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.

12. Physics 151: Lecture 21, Pg 11 Example l A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2x10 7 m. If the radius of Roton is 5.0x10 6 m, what is the magnitude of the free-fall acceleration on the surface of Roton? l a. 31 m/s 2 l b. 27 m/s 2 l c. 34 m/s 2 l d. 40 m/s 2 l e. 19 m/s 2

13. Physics 151: Lecture 21, Pg 12 FLUIDS: Example l 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. l (a) Find the maximum height through which he can lift the water.

14. Physics 151: Lecture 21, Pg 13 A1A1 A 20 M dCdC A1A1 A 10 M dAdA A) d A = (1/2)d C B) d A = d C C) d A = 2d C Lecture 29, ACT 2b Hydraulics l Consider the systems shown to the right. çIn each case, a block of mass M is placed on the piston of the large cylinder, resulting in a difference d I in the liquid levels.  If A 10 = 2  A 20, compare d A and d C.

15. Physics 151: Lecture 21, Pg 14 Lecture 29, ACT 3 Buoyancy l 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. çIf you turn the styrofoam+Pb upside down, what happens? styrofoam Pb A) It sinks C)B)D) styrofoam Pb

16. Physics 151: Lecture 21, Pg 15 Example l 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. l What is the speed with of the liquid as it leaves the tank. h v=? 

17. Physics 151: Lecture 21, Pg 16 Venturi Meter v = ? Can we know what is v from what we can measure ? h A 1, A 2  Hg  air

18. Physics 151: Lecture 21, Pg 17 Example l 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-cm 3 container in 16.3 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. d = 0.247 cm

19. Physics 151: Lecture 21, Pg 18 Simple Harmonic Motion Lecture 31, Act 3 l You are sitting on a swing. A friend gives you a small push and you start swinging back & forth with period T 1. l Suppose you were standing on the swing rather than sitting. When given a small push you start swinging back & forth with period T 2. çWhich of the following is true: (a) T 1 = T 2 (b) T 1 > T 2 (c) T 1 < T 2

20. Physics 151: Lecture 21, Pg 19 Lecture 31, Act 4 Simple Harmonic Motion l 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.

21. Physics 151: Lecture 21, Pg 20 Lecture 31, Act 4 Period (a)(b)(c) l What length do we make the simple pendulum so that it has the same period as the rod pendulum? LRLR LSLS

22. Physics 151: Lecture 21, Pg 21 Lecture 33, Act 1 Resonant Motion l Consider the following set of pendula all attached to the same string D A B C If I start bob D swinging which of the others will have the largest swing amplitude ? (A)(B)(C)

23. Physics 151: Lecture 21, Pg 22 Which of the graphs on the right shows a wave where the frequency and wave velocity are both doubled ? WAVES: Example The figure on the right shows a sine wave on a string at one instant of time.

24. Physics 151: Lecture 21, Pg 23 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)] Example

25. Physics 151: Lecture 21, Pg 24 For the transverse wave described by y = 0.15 sin [  (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 Example

26. Physics 151: Lecture 21, Pg 25 Lecture 35, Act 2 Wave Power l 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. P final /P init = X (a) 1/4 (b) 1/2 (c) 1 (d) 2 (e) 4 initial final

27. Physics 151: Lecture 21, Pg 26 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 Lecture 35, Act 4 Traveling Waves Can you determine the relative amplitudes of the transmitted and reflected waves ?

28. Physics 151: Lecture 21, Pg 27 Additional Simple Problems

29. Physics 151: Lecture 21, Pg 28 GRAVITY: Force and acceleration l 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 ? l You are told that R X ~ 20 R Earth and M X ~ 300 M Earth. (a) 0.75 (b) (c) (a) 0.75 W (b) 1.5 W (c) 2.25 W E X

30. Physics 151: Lecture 21, Pg 29 Lecture 28, Act 2 Satellite Energies l 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) 1/2 (b) (c) (a) 1/2 (b) 3/4 (c) 4/3 (d) 3/2 (e) 2

31. Physics 151: Lecture 21, Pg 30 Example l 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, l a. its speed is constant. l b. its speed is increasing. l c. its speed is decreasing. l d. its speed is a maximum. l e. its speed is a maximum. Animation

32. Physics 151: Lecture 21, Pg 31 Example l 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)

33. Physics 151: Lecture 21, Pg 32 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 (  oil <  ball <  water ) is slowly added to the container until it just covers the ball. l çRelative to the water level, the ball will: water oil (A) move up (B) move down (C) stay in same place See text: 14.4

34. Physics 151: Lecture 21, Pg 33 A1A1 A 10 M dAdA A2A2 M dBdB A) d A =(1/2)d B B) d A = d B C) d A = 2d B Lecture 29, ACT 2a Hydraulics l Consider the systems shown to the right. çIn each case, a block of mass M is placed on the piston of the large cylinder, resulting in a difference d I in the liquid levels.  If A 2 = 2  A 1, compare d A and d B.

35. Physics 151: Lecture 21, Pg 34 Example l 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?

36. Physics 151: Lecture 21, Pg 35 Lecture 32, Act 3 Period l 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) RRRR A) B) C) D)

37. Physics 151: Lecture 21, Pg 36 Lecture 34, Act 1 Wave Motion l 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. l Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. çWhat 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

38. Physics 151: Lecture 21, Pg 37 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 Example

39. Physics 151: Lecture 21, Pg 38 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 -  t ) l Which of the following equation describes a harmonic wave moving in the negative x direction ? (a) y(x,t) = A sin (  kx   t ) (b) y(x,t) = A cos ( kx   t ) (c) y(x,t) = A cos (  kx   t )

40. Physics 151: Lecture 21, Pg 39 Lecture 34, Act 4 Wave Motion l A heavy rope hangs from the ceiling, and a small amplitude transverse wave is started by jiggling the rope at the bottom. l As the wave travels up the rope, its speed will: (a) increase (b) decrease (c) stay the same v l Can you calcuate how long will it take for a pulse travels a rope of length L and mass m ?