This assignment is worth 20 points. Each part is worth 1 point, except for the last problem, in which each part is worth half a point.

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1 1 of 6 11/20/2009 3:43 PM 0/20 Tue Dec :15 PM EST Question Points /20/20/30/10/30/10/20/20/4 Total 0/20 Description This assignment is worth 20 points. Each part is worth 1 point, except for the last problem, in which each part is worth half a point. Assume the numbers given in each problem are accurate to three significant figures. WebAssign expects your answers to be accurate within 1%. If you don't round off until the end, and then round off to three significant figures, you should be fine. Occasionally there are errors in WebAssign. If you are convinced your answer is correct and WebAssign is grading you incorrectly please check with Professor Duffy. 1. 0/2 pointswiley Simulation 5.3. [ ] Universal Gravitation This simulation shows a satellite orbiting a planet. The planet has a much larger mass than the satellite, The sliders allow you to adjust the initial speed of the satellite; the initial distance between the satellite and the center of the planet; and the mass of the satellite. After running the simulation, hit the Reset button if you want to adjust any of the sliders. Given the limits on the sliders available to you in the simulation, determine the following:

2 2 of 6 11/20/2009 3:43 PM (a) The maximum elasped time displayed by the simulation for one orbit (b) The maximum value displayed by the simulation for the speed of the satellite /2 pointsduffy_ep_ch08_likech16p56 [ ] Three balls, with masses of m, 2m, and 3m, are placed at the corners of a square measuring L on each side, as shown in the figure. The value of m is 2.60 kg, and L = 70.0 cm. Assume this set of three balls is not interacting with anything else in the niverse. Note that, on WebAssign, a number like can be entered as 4.56e-5 a) What is the magnitude of the net gravitational force acting on the ball of mass 2m? 5.82e-09 N (b) What is the magnitude of the net gravitational force acting on the ball of mass 3m? 6.57e-09 N. 0/3 pointswiley Simulation 15.2b. [ ] imple Harmonic Motion

3 3 of 6 11/20/2009 3:43 PM Note: After running the simulation, press the Reset button if you want to adjust the sliders. (a) The spring is at its natural length when the block is placed at what position? 8 cm Consider the following three cases, all of which have the same spring constant: Case 1: the block mass is 0.20 kg; the initial position is 0.05 m, and damping is off. Case 2: the block mass is 0.40 kg; the initial position is 0.05 m, and damping is off. Case 3: the block mass is 0.20 kg; the initial position is 0.14 m, and damping is off. Damping, by the way, is essentially friction, so damping being off means that there is no friction. (b) Rank the cases based on the total mechanical energy of the spring-mass system 2 seconds after the block is released from rest, from largest to smallest. Use only > and/or = signs in your ranking (e.g., 1>2=3). 3>1=2 -or- 3>2=1 (c) Rank the cases based on the oscillation frequency of the spring-mass system, from largest to smallest. Use only > and/or = signs in your ranking (e.g., 1>2=2). 1=3>2 -or- 3=1>2 4. 0/1 pointsduffy_ep_ch12_p101 [ ] wo blocks are held together, with a compressed spring between them, on a horizontal frictionless surface. When the system s released, the spring pushes the blocks apart and they then move off in opposite directions. The spring remains behind, and ou can assume that all of its energy is transformed to the kinetic energy of the blocks. The mass of block A is 3.00 times the ass of block B, and the energy stored in the spring was 220. J. What is the kinetic energy of block A after it is no longer in ontact with the spring? See if you can work this out without a calculator.

4 4 of 6 11/20/2009 3:43 PM 55 J 5. 0/3 pointsduffy_ep_ch12_p102 [ ] A block with a mass of kg is placed on a horizontal frictionless surface, and then attached to a spring with a spring onstant of 3.00 N/m. The system is then set into motion, so that the block experiences simple harmonic motion with an mplitude of 10.0 cm. a) Find the speed of the block when it is a distance of 7.00 cm from the equilibrium position m/s b) Find the magnitude of the block's acceleration when the block is at a distance of 7.00 cm from the equilibrium position m/s 2 (c) Find the smallest amount of time it takes the block to move from a position of 10.0 cm from equilibrium to a position that is just 7.00 cm from equilibrium s. 0/1 pointsduffy_ep_ch12_p103 [ ] A simple pendulum consists of a small ball tied to the ceiling of an elevator by a light string. The string has a length of 1.30 m, nd the elevator has an acceleration of 1.40 m/s 2, directed up. Use g = 9.80 m/s 2. What is the period of the oscillations of this pendulum? Assume that the oscillations have a small amplitude s. 0/2 pointswiley Simulation 9.2. [208581] endulum motion Note that the graph labeled "Velocity" shows the angular velocity, and the graph labeled "Acceleration" shows the angular acceleration. (a) You have a simple pendulum in your room, and you would like to adjust its period. You can do that either by changing the

5 5 of 6 11/20/2009 3:43 PM ass, changing the length, or changing the maximum angle from which you let it go (although you keep that maximum angle elow 40 ). One of these changes makes no difference to the period, one makes a very small difference, and the third makes noticeable difference. Which is which? Changing the mass makes no difference; changing the length makes a small difference; and changing the maximum angle makes a noticeable difference. Changing the mass makes no difference; changing the maximum angle makes a small difference; and changing the length makes a noticeable difference. Changing the length makes no difference; changing the mass makes a small difference; and changing the maximum angle makes a noticeable difference. Changing the length makes no difference; changing the maximum angle makes a small difference; and changing the mass makes a noticeable difference. Changing the maximum angle makes no difference; changing the length makes a small difference; and changing the mass makes a noticeable difference. Changing the maximum angle makes no difference; changing the mass makes a small difference; and changing the length makes a noticeable difference. (b) Rank these cases by their frequency of oscillation, from largest to smallest. Case 1: Gravitational acceleration = g; length = L Case 2: Gravitational acceleration = 2g; length = L Case 3: Gravitational acceleration = g; length = 2L Case 4: Gravitational acceleration = 2g; length = 2L Use only > and/or = signs in your ranking (e.g., 4>2>1=3). 2>1=4>3 -or- 2>4=1>3 8. 0/2 pointsduffy_ep_ch09_p21 [ ] A low-density block with a weight of 10.0 N is placed in a beaker of water and tied to the bottom of the beaker by a vertical tring of fixed length. When the block is 25% submerged, the tension in the string is 19.0 N. The string will break if its tension xceeds 70.0 N. As water is steadily added to the beaker, the block becomes more and more submerged. (a) What percentage of the block is submerged at the instant the string breaks? 69 % b) After the string breaks and the block comes to a new equilibrium position in the beaker, what fraction of the block s volume s submerged? 8.62 %. 0/4 pointsduffy_ep_ch09_p101 [ ]

6 6 of 6 11/20/2009 3:43 PM In Figure A, a ball with a weight of 24.0 N is supported by a string. The ball hangs over a beaker of fluid. The beaker sits on a scale, which reads 18.0 N. n Figure B, the ball is completely submerged in the fluid, and the tension in the string is 10.0 N. In Figure C, the ball is exactly half submerged. In Figure D, the string has been cut, and the ball is resting at the bottom of the beaker. In each picture, the ball is in equilibrium. (a) In Figure A, determine the magnitude of the tension in the string. 24 N b) In Figure B, determine the magnitude of the buoyant force acting on the ball. 14 N c) In Figure B, what is the scale reading? 32 N d) In Figure C, determine the magnitude of the buoyant force acting on the ball. 7 N (e) In Figure C, determine the magnitude of the tension in the string. 17 N f) In Figure C, what is the scale reading? 25 N g) In Figure D, determine the magnitude of the buoyant force acting on the ball. 14 N h) In Figure D, what is the scale reading? 42 N Assignment Details