A piece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm

A piece of lead has the shape of a hockey puck, with a...

A piece of lead has the shape of a hockey puck, with a diameter
of 7.5 $\mathrm{cm}$ and a height of 2.5 $\mathrm{cm}$ . If the puck is placed in a mercury
bath, it floats. How deep below the surface of the mercury is the
bottom of the lead puck?

Key Concepts

Buoyancy Equilibrium

Buoyancy equilibrium is achieved when the upward buoyant force exerted by the displaced fluid equals the weight of the object. This concept is used to calculate the submerged volume of an object, leading to the determination of how deeply it sinks in the fluid.

Volume Calculation for Cylindrical Shapes

Calculating the volume of a cylinder requires understanding the formula V = ?r²h, where 'r' is the radius and 'h' is the height. This is important for determining the amount of fluid displaced by a cylindrical object, which is directly related to the buoyant force it experiences.

Archimedes' Principle

This principle of fluid mechanics states that any object submerged in a fluid experiences an upward force equal to the weight of the fluid it displaces. It is the foundation for understanding why and how objects float, and is critical in determining the equilibrium condition for submerged bodies.

Density

Density, defined as mass per unit volume, is an essential concept that determines whether an object will float or sink when placed in a fluid. By comparing the density of the object with the density of the fluid, one can predict the degree of submersion or flotation.

Transcript

00:01 So the question this time, question 49, a piece of lead has the shape of a hockey puck with a diameter of 0 .75 meters, that's 7 .5 centimeters and a height of 2 .5 centimeters convert into meters as we need to.

00:20 So if the puck is placed in a mercury bath, it floats how deep below the surface of the mercury is the bottom.

00:30 Once again i stated before that percentage of an object submerged is equal to a ratio of the density of the object floating, density of our solid, divided by the density of the fluid.

00:52 This is again very straightforwardly proven when we have the weight is equal to the buoyancy force in the case of something floating.

01:03 So obviously density of our solid times the volume of our solid multiplied by g.

01:17 Is equal to the density of our fluid, multiplied by the volume submerged, multiplied by g.

01:29 We can't sort the g's and rearrange the volume submers over the total volume, the solid, is equal to the density of the solid by the density of the fluid.

01:48 I've used water here.

01:50 Where the principle holds.

01:54 So with this knowledge, we're very much talking about the volume.

02:02 Merged is what we're after.

02:11 And that's going to equal the total volume, multiplied by the ratio of the densities.

02:18 In this case, we're talking about a lead hockey puck and a mercury fluid.

02:28 So we use their chemical symbols, pb, density of pb, density of hg.

02:39 So what about our volumes? so we imagine, with our circular hockey puck, its volume is equal to pi times its radius squared...