A ball having a diameter of 0.6 m and a mass of 0.35 kg is falling in the atmosphere at 10^∘ C

A ball having a diameter of 0.6 m and a mass of 0.35 kg is...

Key Concepts

Force Equilibrium

Force equilibrium in the context of falling objects refers to the condition where the downward gravitational force is exactly counterbalanced by the upward drag force. This balance of forces results in no further acceleration and a constant falling speed, which is the terminal velocity.

Fluid Properties

Fluid properties such as density and viscosity are critical in determining the magnitude of the drag force. The density of the fluid influences how much resistance an object encounters as it falls, and changes in these properties, such as variations with temperature, can affect the terminal velocity.

Terminal Velocity

Terminal velocity is the constant speed that a freely falling object eventually reaches when the drag force (air resistance) acting on it equals the gravitational force pulling it downward. At terminal velocity, the net acceleration of the object is zero, indicating a balance between driving and resisting forces.

Drag Force

Drag force is the resistance force exerted by a fluid (such as air) on an object moving through it. This force typically depends on the object's velocity, cross-sectional area, drag coefficient, and the density of the fluid, and it acts in the opposite direction to the object's motion.

Transcript

00:01 And this problem is asked to consider a ball falling in the atmosphere.

00:04 We were asked to find terminal velocity.

00:06 We're given all of the information here.

00:08 Diameter.

00:10 Did i not write my mass? there's my mass.

00:13 Sorry about that.

00:14 Our temperature, from the temperature, i looked up our kinematic viscosity and our density of air, and we know g, acceleration due to gravity.

00:22 So here's my ball, and i've got a force acting down.

00:27 My buoyant force is acting up.

00:29 And my drag is acting up.

00:33 So we've got these are summation of fy as to equal zero.

00:38 So i know that my buoyant force plus my drag force will equal my weight.

00:49 Okay, buoyant force is defined as b times v times g.

00:58 And v will be equal to four thirds pi r, which will be over two cubed.

01:12 Okay.

01:14 So my buoyant force, do i want to finish that yet? my buoyant force will be equal to times v is four thirds pi times 0 .6 divided by 2 cubed times 9 .81 meters per second squared.

01:55 So my buoyant force will be equal to 1 .3835 newton's.

02:03 That's my buoyant force.

02:06 Now let's do my drag force.

02:11 My force of my drag will be equal to one half density, and this will be cdau squared, where a is equal to pi d over two squared, and my reynolds number will be equal to ud over my kinematic.

02:39 Okay, so let's do where i'm running...

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