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Various physics problems and questions from the 'physics: concepts and connections' textbook by hobson, including calculations of net force and mass of the earth, analysis of energy transfer in an animation, and conceptual questions related to gravity and potential energy.
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Phys 100 Spring 2009
Due: 4 March 2009
1 Hobson, Physics: Concepts and Connections, Ch. 5, Conceptual Question 2, page 111.
2 Hobson, Physics: Concepts and Connections, Ch. 5, Conceptual Question 18, page 112. Be as specific as you can. Does the weight stay the same, increase or decrease?
3 Hobson, Physics: Concepts and Connections, Ch. 5, Problem 6, page 113.
4 Hobson, Physics: Concepts and Connections, Ch. 5, Problem 8, page 113. Compare the answer to that of problem 6. Which object (moon or sun) exerts the dominant gravitational force on the earth?
5 Measuring the mass of the earth
The radius of the earth can be determined by geometrical observations and currently the most accurate average value is 6. 4 × 106 m. What about the earth’s mass? This can be calculated using experimental data as follows. Consider an object of mass 5.0 kg on the surface of the earth.
a) Calculate the net force exerted on the object due to the earth’s gravitational force (this does not use the mass of the earth). Which constant quantity used in this calculation would need to be measured experimentally? b) Use the result from the previous part and Newton’s Universal Law of Gravitation to calculate the mass of the earth. Which constant quantity used in this calculation would need to be measured experimentally? c) Would you describe the above method as a direct or indirect way of determining the earth’s mass? Does it depend on any measurements for success or is it purely theoretical?
6 Hobson, Physics: Concepts and Connections, Ch. 6, Review Question 12, page 131.
7 Hobson, Physics: Concepts and Connections, Ch. 6 Problem 10, page 134.
Assume that the runner has mass 60 kg.
8 Energy and a Skater
Running the Animation: The following exercise will require the animation “Energy Skate Park” provided by the PhET group. There will generally be two parts to this:
The animation can be accessed at one of the following locations:
http://phet.colorado.edu/sims/energy-skate-park/energy-skate-park.jnlp
http://home.mesastate.edu/∼dacollin/teaching/2009Spring/Phys100/animations/skater.jar
In each case you will be prompted to open the animation with Java. Open the animation. A track that runs down and up should appear. A skater will move on this track. There are a number of adjustable controls in the panel on the right. Ensure that the location is “Earth” and that the gravity is 9. 81. There should be no friction. The panel at the bottom controls the speed of the animation and you can freeze it by hitting “pause.”
a) Hit “Bar Graph” in the panel on the right. This will produce a separate window which lists three types of energy plus a total energy. Observe this while the skate is moving. As the skater descends, does the kinetic energy increase, decrease or stay the same? As the skater ascends does the kinetic energy increase, decrease or stay the same? When is the kinetic energy largest? b) As the skater descends, does the potential energy increase, decrease or stay the same? As the skater ascends does the potential energy increase, decrease or stay the same? When is the potential energy largest? c) As the skater descends, does the total energy increase, decrease or stay the same? As the skater ascends does the total energy increase, decrease or stay the same? d) In order to extract numbers for the energies, hit “Energy vs. Time” in the panel on the right. This will produce a separate window which graphs the energies. Hit “Clear” in this window and let the animation run so that the skater moves up and down several times. Several graphs should appear. Hit “Pause” in this window. Now hit playback and stop this when the skater is at the highest point. Record the potential energy (PE) and kinetic energy (KE) and use these to determine the total energy. e) Stop the playback when the skater is midway down the slope, record PE, KE and use these to determine the total energy. How do these compare to the numbers at the highest point of the track? Repeat this for the bottom and the midpoint on the way up. f) Based on these observations, what can you conclude about the total energy of the skater at all times?
Now consider this for a more complicated track. Click the “Tracks” menu item and hit “Double Well (Roller Coaster)”. This will open a new track to which the skater sticks.
g) Hit “Energy vs. Time” and clear the graphs. Let the skater move along the entire track at least once. Hit “Pause.” Stop the playback when he reaches the highest point. Record PE, KE and determine the total energy. Repeat this at the bottom of each the two dips. At which point is the kinetic energy largest and at which point is it smallest? At which point is the potential energy largest and at which smallest? What can you conclude about the total energy of the skater at all times?