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Chapter 8: Problem 45

Find the \(x\) - and \(y\) -coordinates of the center of mass of the flat triangular plate of height \(H=17.3 \mathrm{~cm}\) and base \(B=10.0 \mathrm{~cm}\) shown in the figure.

Short Answer

Expert verified
Answer: The coordinates of the center of mass of the flat triangular plate are (5, 5.77) cm.

Step by step solution

01

Identify the coordinates of the vertices of the triangle

We can consider the base of the triangle to be along the x-axis and one vertex of the triangle at the origin. Then, the vertices of the triangle are A(0, 0), B(10, 0), and C(5, 17.3).
02

Calculate the x-coordinate of the center of mass

The x-coordinate of the center of mass of a flat triangular plate is given by the average of the x-coordinates of its vertices. So, we can find the x-coordinate of the center of mass using the formula: \(x_{c} = \frac{A_x + B_x + C_x}{3}\) Now substitute the x-coordinates of the vertices A(0), B(10), and C(5) in the above formula: \(x_{c} = \frac{0 + 10 + 5}{3} = \frac{15}{3} = 5 \mathrm{~cm}\)
03

Calculate the y-coordinate of the center of mass

Similarly, the y-coordinate of the center of mass of a flat triangular plate is given by the average of the y-coordinates of its vertices. So, we can find the y-coordinate of the center of mass using the formula: \(y_{c} = \frac{A_y + B_y + C_y}{3}\) Now substitute the y-coordinates of the vertices A(0), B(0), and C(17.3) in the above formula: \(y_{c} = \frac{0 + 0 + 17.3}{3} = \frac{17.3}{3} = 5.77 \mathrm{~cm}\)
04

State the coordinates of the center of mass

The coordinates of the center of mass of the flat triangular plate are \((x_c, y_c) = (5, 5.77)\).

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Most popular questions from this chapter

The density of a \(1.00-\mathrm{m}\) long rod can be described by the linear density function \(\lambda(x)=\) \(100 \cdot \mathrm{g} / \mathrm{m}+10.0 x \mathrm{~g} / \mathrm{m}^{2}\) One end of the rod is positioned at \(x=0\) and the other at \(x=1.00 \mathrm{~m} .\) Determine (a) the total mass of the rod, and (b) the center-of-mass coordinate.

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