A solid cylinder sits on top of a solid cube as shown in Figure P7.18. How far above the table's

step 1 Okay, welcome back. So in this one, we're given an image of two objects and we're given their ma

A solid cylinder sits on top of a solid cube as shown in...

Key Concepts

Centroid of Geometric Shapes

The centroid is the geometric center of a simple shape, and for regularly shaped solids, such as cubes and cylinders, the centroid is located at a well-defined point (for instance, the center of a cube or the midpoint along the height of a cylinder). This property is fundamental when determining the center of mass for composite bodies, as these standard shapes serve as building blocks.

Weighted Average

The weighted average is a mathematical method used to find the center of mass of a composite body. It involves multiplying the mass of each component by its respective position (distance from a reference point) and then dividing the total by the sum of the masses, thereby accounting for the varying contributions of different parts.

Center of Mass / Center of Gravity

The center of mass (or center of gravity) is the point in an object or system where the entire mass can be considered to be concentrated. For a uniform gravitational field, it is the point at which the weight can be assumed to act, simplifying calculations of balance and stability in static systems.

Composite Bodies

Composite bodies are objects made up of simpler shapes whose individual centers of mass are known or easily determined. In problems involving composite bodies, the overall center of mass is calculated by considering the contribution of each component's mass and position, allowing for the treatment of complex shapes as a combination of simpler parts.

Transcript

0:00 Okay, welcome back.

00:01 So in this one, we're given an image of two objects and we're given their masses as well as something about their dimensions.

00:09 And it tells us to find the, find how far above the service of the table the center of gravity is.

00:16 Now, these are extended objects, but because they're solid, we can view their centers of gravity as being right in the middle.

00:24 So this, this 800 gram cube here, it's like it has a sense.

00:30 Center of gravity that's right in the middle there and that would be you know at 2 .5 centimeters above and the 4 .400 gram object well it's got a it's like it's center of gravity is right in the middle and it's 2 .5 above the cube and the cube is five up so this would be 7 .5 centimeters right there so that is that's that's kind of how we get started with this one and then we're just going to use the formula for the y coordinate of the center of gravity.

01:03 So y center of gravity, and that's going to be equal to y1, m1, plus y2, m2, all over m1 plus m2.

01:15 Now, it doesn't matter which one we let by1 and which one we let by2.

01:19 I'm just going to have the cube by1 and the sphere by2, or m1, whatever.

01:26 So for the cube, our y is also, we should probably convert these to si, just to be clear.

01:37 It doesn't really matter in this case.

01:39 If we didn't, it would be, it would just give us our answer back in centimeters, which we'll probably convert to anyway.

01:46 But it's a good habit to turn these into si when you're doing these things...

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