A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?

Question

Mathematics

Haven Buchanan

30 January, 02:49

A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?

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Answers (1)

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Silas · Answer 1

This problem can be solved in two ways, the long way, or the short way.

1. The long way

We know that the base of the triangle is along the x-axis, and the length of the base is 20.

The centre of mass is located at 2/3 of the distance from vertex (3,4) along the median, which cuts the base at (10,0).

Therefore the centre of mass is located at

x=3 + (10-3) * 2/3=23/3

y=4/3

2. The short way

It turns out that the centre of mass of a triangle sheet is located at the mean of the coordinates of the three vertices, i. e.

CG = ((0+20+3) / 3, (0+0+4) / 3) = (23/3, 4/3) as before.