Statics: Lesson 41 - How to Find Center of Mass for Composite Bodies

Hinzugefügt: 2026-05-05

[00:00:00]divide this into some shapes here.

[00:00:02]And let's see if I got a red pen in my pocket.

[00:00:05]Hello, puppet.

[00:00:07]Okay, here we go. Shape one, the triangular prism. Shape two, the rectangle. And then shape three will be the cylinder up on the top there, okay?

[00:00:17]So, here we go.

[00:00:18]I've got three shapes. 1 2 3.

[00:00:22]And then what do I have? Oh, lordy.

[00:00:26]I got X bar, Y bar, Z bar, M XM YM and ZM.

[00:00:37]Okay, so here's my table.

[00:00:40]Let me make my table nice and beautiful.

[00:00:47]Okay?

[00:00:51]Now, all we have to do is fill that up with the correct values, and we'll be good to go, right? How do you find mass?

[00:00:57]How do you find mass?

[00:00:58]Remember this is pounds per cubic inch.

[00:01:02]So, that's the density.

[00:01:04]I've got to multiply that by the volume, and then I'll have the amount of pounds.

[00:01:09]And then and pounds is going to be pounds mass, okay?

[00:01:13]All right, so real quick, let's go ahead and find the volumes of these three shapes. We'll multiply it by those densities, and then that will get this column here filled in for the mass of shape one, two, and three, okay? So, shape one, remember how to find the volume of a triangular prism? It's the area of one side times the thickness, okay? So, this will be 3 * 3 is 9 / 2 is 4.5.

[00:01:39]So, shape one is going to be 3 * 3 * 4.5 * 1/2, right? Base * height * 1/2 * Oh, 4.5, where did that come from?

[00:01:53]Okay? * 8.

[00:01:56]Okay?

[00:01:57]So, there's number one.

[00:02:00]Okay? And number two, what's number two here?

[00:02:04]Number two is this guy, which is 4 * 4 is 16 * 8. So, 16 * 8. And number three is what?

[00:02:15]So, let's see. 3 * 3 is 9. 9 * 8 is uh 72 * 1/2 is 36.

[00:02:27]And this guy is what uh 80 + 48 is 128.

[00:02:34]And this is inches cubed, inches cubed, and then the last one is the cylinder, which is pi r squared. R is one * the height * 3.

[00:02:50]Okay?

[00:02:51]And