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Lesson Worksheet: The Negative Mass Method Mathematics
In this worksheet, we will practice finding the center of gravity of a lamina that contains holes using the negative mass method.
An equilateral triangle has a side length of 82 cm. When three equal masses are placed at the vertices of the triangle, the centre of mass of the system is . When the mass at vertex is removed, the centre of mass of the system is . Find the coordinates of the centre of mass of the two systems and .
A uniform lamina is in the form of a rectangle , where and . Two points and are on such that . The triangle , where is the center of the rectangle, is cut out of the lamina. Find the coordinates of the center of mass of the resulting lamina. Given that the lamina was freely suspended from , find the tangent of the angle that makes to the vertical, , when the lamina is hanging in its equilibrium position.
A uniform square-shaped lamina of side length 222 cm has a mass of one kilogram. The midpoints of , , and are denoted by , , and respectively. The corners and were folded over so that they lie flat on the surface of the lamina. Bodies of masses 365 g and 294 g were attached to the points and respectively. Find the coordinates of the center of mass of the system rounding your answer to two decimal places if necessary.