Answers must be submitted by 8:00 am Friday, Dec 14, 2007.
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1. Describe the shape of the path taken by the center of gravity of an object that is thrown into the air with a spin (one word)
2. Describe the shape of the path taken by the center of gravity of an object that slides on a smooth horizontal surface while spinning (two words).
3. This question refers to Problem 28 at the end of CP Chapter 10. Which truck(s) will topple ? Choose all that apply:
Truck A
Truck B
Truck C
Explain (in 12 words or fewer) your choices:
4. In what situation is an object’s center of gravity not the same as the object’s center of mass ? (12 words or fewer)
5. What do we call a string and weight that can be suspended ? (2 words).
6. If you suspend an object from a point so that the object is free to swing around that point, where will the object’s center of mass be located once the object stops swinging ? (5 words or fewer)
The textbook defines an object’s center of mass as being “the average position of all the particles of mass that make up an object.” If we think of an object as being made up of a set of masses m1, m2, m3, … etc. whose positions (relative to some coordinate system that you define) are d1, d2, d3, … etc. then the mathematical expression for calculating the position of the center of mass of the object is the “weighted average”:
dCM = (m1d1 + m2d2 + m3d3 + …)/(m1 + m2 + m3 + …)
Use this definition of the center of mass position to answer the following questions.
7. a. Find the coordinates of the center of mass of the system of masses shown below. Do each coordinate separately, first using all the x-coordinates, then all the y-coordinates. Use the given masses with each coordinate set.
xcm = , ycm = b. Imagine a new coordinate system whose origin is located at the 1 kg object and whose axes are parallel to those of the original coordinate system. In this new system the coordinates of the particles are: 3 kg, (-2,-3); 1 kg, (0,0); 5 kg, (3,-3); 6 kg, (3,2). Find the coordinates of the center of mass in this new coordinate system. Xcm = , Ycm = c. Is the physical location of the center of mass found in part (b) any different from that found in part (a)? Explain (in 12 words or fewer) ! (you might find it helpful to sketch the diagram and the two sets of coordinate axes on top of each other to see what's going on here).
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