Chapter 7. Position of the center of mass of a system (7-28)

Question

lJHsIWZpQAqD7/Kiug7dLHqV0hMz7UyVM2e3nF/vK7CwbiaIfiw0vNfTrigwlhCvJjvMwguvRWqjh7eqLfhhDw==
{"title":"Position of the center of mass of a system of N objects","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,8,12,24\"}]"} {"title":"m sub i = masses of the individual objects","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"39,1,52,18\"},{\"shape\":\"rect\",\"coords\":\"77,3,98,16\"},{\"shape\":\"rect\",\"coords\":\"123,4,146,15\"},{\"shape\":\"rect\",\"coords\":\"189,2,215,16\"}]"} {"title":"x sub i = positions of the individual objects","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"53,9,68,23\"},{\"shape\":\"rect\",\"coords\":\"99,7,112,23\"},{\"shape\":\"rect\",\"coords\":\"148,8,160,24\"},{\"shape\":\"rect\",\"coords\":\"214,8,230,23\"}]"} {"title":"Total mass of all N objects together","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"33,14,53,29\"}]"}

Question

V3s+zFEph0udFk9EANQLdg8q+LWLHtE9PwDPbpZoq0g1muY7bWxdoF93gf6kvwQw
{"title":"Position of the center of mass of a system of N objects","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,8,12,24\"}]"} {"title":"m sub i = masses of the individual objects","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"39,1,52,18\"},{\"shape\":\"rect\",\"coords\":\"77,3,98,16\"},{\"shape\":\"rect\",\"coords\":\"123,4,146,15\"},{\"shape\":\"rect\",\"coords\":\"189,2,215,16\"}]"} {"title":"x sub i = positions of the individual objects","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"53,9,68,23\"},{\"shape\":\"rect\",\"coords\":\"99,7,112,23\"},{\"shape\":\"rect\",\"coords\":\"148,8,160,24\"},{\"shape\":\"rect\",\"coords\":\"214,8,230,23\"}]"} {"title":"Total mass of all N objects together","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"33,14,53,29\"}]"}

Question

asS7pGX/sKsHqnohhzbfBxPRwaNj7/IomMj3N9jkuu0Z0Rw/O1jGa6x9w4JN3gZACmqzaw==
{"title":"Position of the center of mass of a system of N objects","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,8,12,24\"}]"} {"title":"m sub i = masses of the individual objects","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"39,1,52,18\"},{\"shape\":\"rect\",\"coords\":\"77,3,98,16\"},{\"shape\":\"rect\",\"coords\":\"123,4,146,15\"},{\"shape\":\"rect\",\"coords\":\"189,2,215,16\"}]"} {"title":"x sub i = positions of the individual objects","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"53,9,68,23\"},{\"shape\":\"rect\",\"coords\":\"99,7,112,23\"},{\"shape\":\"rect\",\"coords\":\"148,8,160,24\"},{\"shape\":\"rect\",\"coords\":\"214,8,230,23\"}]"} {"title":"Total mass of all N objects together","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"33,14,53,29\"}]"}

Question

0jvhAxGUNb8QWQeSF389qIVvPY6V343hINjA2hMBifbnjVmTi4WkME0SXPE=
{"title":"Position of the center of mass of a system of N objects","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,8,12,24\"}]"} {"title":"m sub i = masses of the individual objects","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"39,1,52,18\"},{\"shape\":\"rect\",\"coords\":\"77,3,98,16\"},{\"shape\":\"rect\",\"coords\":\"123,4,146,15\"},{\"shape\":\"rect\",\"coords\":\"189,2,215,16\"}]"} {"title":"x sub i = positions of the individual objects","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"53,9,68,23\"},{\"shape\":\"rect\",\"coords\":\"99,7,112,23\"},{\"shape\":\"rect\",\"coords\":\"148,8,160,24\"},{\"shape\":\"rect\",\"coords\":\"214,8,230,23\"}]"} {"title":"Total mass of all N objects together","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"33,14,53,29\"}]"}

Review

The mass of each individual object represents a fraction \(m_i/M\) of the total mass. Now suppose the \(N\) objects are at different positions along the \(x\) axis: \(x_1\), \(x_2\), \(x_3\), . . . , \(x_N\). (Figure 7-20). By analogy to Equation 7-26, we write the position of the center of mass as a weighted average of these positions: