Lesson: The Negative Mass Method Mathematics

In this lesson, we will learn how to find the center of gravity of a lamina that contains holes using the negative mass method.

Lesson Plan

Students will be able to

calculate the center of gravity of laminas that contain holes using the negative mass method,
solve applied problems involving the center of gravity of laminas containing holes,
calculate the center of gravity of a lamina where a part is cut and moved to a different position (including examples of corners folded over).

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Worksheet

Q1:

A uniform lamina is in the form of a rectangle , where and . Two points and lie on such that and . A hole of radius 5 cm is drilled at and another of radius 4 cm is drilled at . Find the coordinates of the point on from which the lamina can be hung so that is horizontal when hanging in its equilibrium position. Secondly, find the coordinates of the point on from which the lamina can be hung so that is horizontal when hanging in its equilibrium position. Round your answers to two decimal places if necessary.

Q2:

A uniform wire of length 135 cm was bent around five sides of a regular hexagon . Determine the distance between the center of gravity of the wire and the center of the hexagon.

Q3:

A uniform lamina is in the form of a rectangle in which and . The corner , where is the midpoint of , was cut off. The resulting lamina was freely suspended from the vertex . Determine the measure of the angle the side makes to the vertical when the lamina is hanging in its equilibrium position stating your answer to the nearest minute.