Lesson: The Negative Mass Method

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

Worksheet: 19 Questions

Q1:

A uniform lamina in the form of a rectangle 𝐴𝐡𝐢𝐷 where 𝐴𝐡=37cm and 𝐴𝐷=23cm. Two points 𝐸 and 𝐹 lie on 𝐡𝐷 such that 𝐡𝐹=10cm and 𝐷𝐸=15cm. A hole of radius 5 cm is drilled at 𝐹 and another of radius 4 cm is drilled at 𝐸. Find the coordinates of the point 𝑁 on 𝐴𝐡 from which the lamina can be hung so that 𝐴𝐡 is horizontal when hanging in its equilibrium position. Secondly, find the coordinates of the point 𝐾 on 𝐴𝐷 from which the lamina can be hung so that 𝐴𝐷 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 𝐴𝐡𝐢𝐷𝐸𝐹. 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 𝐴𝐡𝐢𝐷 in which 𝐴𝐡=64cm and 𝐡𝐢=240cm. The corner 𝐴𝐡𝐸, where 𝐸 is the midpoint of 𝐴𝐷, was cut off. The resulting lamina 𝐴𝐢𝐷𝐸 was freely suspended from the vertex 𝐢. Determine the measure of the angle the side 𝐢𝐡 makes to the vertical when the lamina is hanging in its equilibrium position stating your answer to the nearest minute.

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