Because you are taking physics, your friend asks you to explain the detection of gravity waves that was made by LIGO in early 2016. (See the section that discusses LIGO.) To do this, you first explain about Einstein's notion of large masses, like those of stars, causing a curvature of spacetime. (See the section on general relativity.) To demonstrate, you put a bowling ball on your bed, so that it sinks downward and creates a deep depression in the mattress. Your sheet has a checked pattern that provides a nice coordinate system, as shown in the figure below. This is an example of a large mass (the bowling ball) creating a curvature of a flat, two-dimensional surface (the mattress) into a third dimension. (Spacetime is four dimensional, so its curvature is not easily visualized.) Then, you are going to amaze your friend by projecting a marble horizontally along a section of the sheet surface that is curved downward by the bowling ball so that the marble follows a circular path, as shown by the black path of the marble in the figure. The plane of the circular path is horizontal and every point on the path is equidistant from the center of the bowling ball. The marble appears to be in orbit around the bowling ball! Assume that the marble can move with negligible rolling friction on your sheet. The circular path you choose is of radius 10.6 cm at a point on the sheet at which its surface is tilted at 27.5° to the horizontal. You need to determine the speed (in m/s) with which you must project the marble to have it follow the circular path. m/s
Because you are taking physics, your friend asks you to explain the detection of gravity waves that was made by LIGO in early 2016. (See the section that discusses LIGO.) To do this, you first explain about Einstein's notion of large masses, like those of stars, causing a curvature of spacetime. (See the section on general relativity.) To demonstrate, you put a bowling ball on your bed, so that it sinks downward and creates a deep depression in the mattress. Your sheet has a checked pattern that provides a nice coordinate system, as shown in the figure below. This is an example of a large mass (the bowling ball) creating a curvature of a flat, two-dimensional surface (the mattress) into a third dimension. (Spacetime is four dimensional, so its curvature is not easily visualized.) Then, you are going to amaze your friend by projecting a marble horizontally along a section of the sheet surface that is curved downward by the bowling ball so that the marble follows a circular path, as shown by the black path of the marble in the figure. The plane of the circular path is horizontal and every point on the path is equidistant from the center of the bowling ball. The marble appears to be in orbit around the bowling ball! Assume that the marble can move with negligible rolling friction on your sheet. The circular path you choose is of radius 10.6 cm at a point on the sheet at which its surface is tilted at 27.5° to the horizontal. You need to determine the speed (in m/s) with which you must project the marble to have it follow the circular path. m/s
Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN:9781337399920
Author:Michael A. Seeds, Dana Backman
Publisher:Michael A. Seeds, Dana Backman
Chapter5: Gravity
Section: Chapter Questions
Problem 38RQ
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Transcribed Image Text:Because you are taking physics, your friend asks you to explain the detection of gravity waves that was made by LIGO in early 2016. (See the section that discusses LIGO.) To do this, you first explain about Einstein's notion of large masses, like those of stars, causing a curvature of
spacetime. (See the section on general relativity.) To demonstrate, you put a bowling ball on your bed, so that it sinks downward and creates a deep depression in the mattress. Your sheet has a checked pattern that provides a nice coordinate system, as shown in the figure below.
This is an example of a large mass (the bowling ball) creating a curvature of a flat, two-dimensional surface (the mattress) into a third dimension. (Spacetime is four dimensional, so its curvature is not easily visualized.) Then, you are going to amaze your friend by projecting a marble
horizontally along a section of the sheet surface that is curved downward by the bowling ball so that the marble follows a circular path, as shown by the black path of the marble in the figure. The plane of the circular path is horizontal and every point on the path is equidistant from the
center of the bowling ball. The marble appears to be in orbit around the bowling ball! Assume that the marble can move with negligible rolling friction on your sheet. The circular path you choose is of radius 10.6 cm at a point on the sheet at which its surface is tilted at 27.5° to the
horizontal. You need to determine the speed (in m/s) with which you must project the marble to have it follow the circular path.
m/s
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