Lauren

A bowling ball sits on a mattress with a checked pattern bedsheet. The bowling ball makes an indentation on the mattress. A marble is next to the bowling ball. The marble's path around the bowling ball is shown using a curved arrow.

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 11.6 cm at a point on the sheet at which its surface is tilted at 25.5° 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.