A plastic block that has a length of 054 m a width of 027 m...

A plastic block that has a length of 0.54 m, a width of 0.27 m, and a height of 0.33 m, and has a density of 690 kg/m3 floats in both water and oil. (a) If the plastic block is floating at the surface of a tank of water (which has a density of 1000 kg/m3), what is the distance from the top of the block to the surface of the water? m (b)If the plastic block is floating at the surface of a tank of oil (which has a density of 900 kg/m3), what is the distance from the top of the block to the surface of the oil? m

Transcript

00:01 In this video, we're going to be looking at the buoyant force.

00:03 Okay, and what i have is a plastic block.

00:06 I know it's dimensions and i know it's density.

00:09 And i'm going to submerce it or actually float it on the surfaces of water and oil.

00:16 I know there are densities as well.

00:18 And i want to find how far is the distance from the top of the block to the surface of the water and how far is it from the top of the block to the surface of the oil? okay, so let's write down what we know first.

00:32 I know the length of the block l equals 0 .54 meters.

00:41 Okay, i know the width of the block, w.

00:44 That equals 0 .27 meters.

00:50 And i know the height of the block equals 0 .33 meters.

00:58 Okay, and i know the density of the block.

01:01 I'll call that row sub b.

01:04 That equals 690 kilograms per meters cubed.

01:13 I know the density of water.

01:15 Okay, i'll call that row sub w.

01:19 That equals 1 ,000 kilograms per meter cubed.

01:26 And i know the density of our oil, and that is 900 kilograms per meter cubed.

01:34 Meter cubed.

01:37 Okay, so how do i solve this problem? i know that the buoyant force acting on an object equals that object's mass times acceleration due to gravity, so that object's weight when it's in an equilibrium system.

01:51 So when we're floating on the surface of something, okay, we're halfway submerged, well, not halfway, but some percent submerged, some percent above the liquid, whatever liquid we're floating in.

02:06 Okay, so we have our forces acting are the weight of the block.

02:10 So that's m .g in the negative direction.

02:13 The buoyant force, fb, that equals the mass of the, or the weight of the displaced water.

02:19 So m .w.

02:21 Um, times g.

02:24 So when the buoyant force equals the weight of the block, the object will float and we can find out what percentage is below the water.

02:32 So let's first start by finding the mass...