An 800 g steel plate has the shape of the isosceles

Chapter 12, Problem 52P

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QUESTION:

An $800\ g$ steel plate has the shape of the isosceles triangle shown in Figure P12.52. What are the $x$- and $y$-coordinates of the center of mass?

Hint: Divide the triangle into vertical strips of width $dx$, then relate the mass dm of a strip at position $x$ to the values of $x$ and $dx$

Equation Transcription:

$800\ g$

$x$

$y$

$dx$

Text Transcription:

800 g

Questions & Answers

QUESTION:

An $800\ g$ steel plate has the shape of the isosceles triangle shown in Figure P12.52. What are the $x$- and $y$-coordinates of the center of mass?

Hint: Divide the triangle into vertical strips of width $dx$, then relate the mass dm of a strip at position $x$ to the values of $x$ and $dx$

Equation Transcription:

$800\ g$

$x$

$y$

$dx$

Text Transcription:

800 g

ANSWER:

Step 1 of 4

For the given steel plate with mass $M=0.8 \mathrm{~kg}$, we need to calculate the coordinates of the center of mass. The steel plate has the dimensions $b=0.2 \mathrm{~m}$ and $l=0.3 \mathrm{~m}$ with area $A$.

Area of the steel plate,

$A=\frac{1}{2} b l$

$A =\frac{1}{2}(0.2 \mathrm{~m})(0.3 \mathrm{~m})$

$A =0.030 \mathrm{~m}^{2}$

Let us consider a vertical differential element with width $d x$ having mass $d m$, which is at a distance $x$ from the origin. The length of the element is $l$, as shown in the figure below