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:

The table shows the distribution of a system of masses on a uniform lamina.

Which of the following is the center of mass of this system?

Q2:

A uniform lamina of mass 15 kg has its center of mass at . If a piece of the lamina is cut out whose mass is 11 kg and whose center of mass is at , find the coordinates of the center of mass of the remaining part.

Q3:

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 .