A window washer pushes his scrub brush up a vertical window...

A window washer pushes his scrub brush up a vertical window at constant speed by applying a force $\vec{F}$ as shown in Figure 5.74 . The brush weighs $12.0 \mathrm{~N},$ and the coefficient of kinetic friction is $\mu_{\mathrm{k}}=0.150 .$ Calculate (a) the magnitude of the force $\overrightarrow{\boldsymbol{F}}$ and (b) the normal force exerted by the window on the brush.

Key Concepts

Newton's First Law of Motion

Newton's First Law states that an object moving at a constant velocity will continue to do so if the net force acting on it is zero. This concept is essential in problems dealing with constant speed because it allows us to set up balance equations for forces in all directions, ensuring that the sum of forces equals zero.

Kinetic Friction

Kinetic friction is the force that opposes the motion of objects sliding past one another. It is proportional to the normal force and is calculated using the coefficient of kinetic friction. Understanding kinetic friction is crucial when analyzing systems where movement is opposed by resistive forces.

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object resting upon it. It is a key component in determining frictional forces since the frictional force is directly proportional to the normal force. Accurately identifying and calculating the normal force is vital in problems involving forces and friction.

Force Decomposition

Force decomposition is the process of breaking a force into its orthogonal components, typically along the horizontal and vertical directions. This technique is fundamental in analyzing the net forces acting on an object, especially when forces are applied at angles and must be resolved to apply Newton's laws effectively.

Transcript

00:01 So in this question, we have a window washer pushing a brush against the building at an angle of 53 .1 degrees with the force of f.

00:19 And we want to know a couple things.

00:21 We want to know the magnitude of the force f, and we also want to know the magnitude of the normal force that is acting from the window onto the brush.

00:34 So the first thing we have to do is we got to draw our free body diagram.

00:39 So for our brush, we have force of gravity straight down for the brush, normal force, perpendicular to the surface for the brush, and our force f at this angle.

00:58 Now what we have to do, though, is we have to break this f up into its components.

01:02 And the way we can do that is by figuring out the horizontal and the vertical components of that force.

01:10 So the vertical component is going to be opposite hypotenuse.

01:15 So we can change that f, which i'm going to get rid of now.

01:19 We're going to change it up into its components.

01:23 So we're going to make the vertical component f times the sine of 53 .1 degrees.

01:34 And the horizontal component as f cosine 53 .1 degrees.

01:48 Now it tells us, and this is important, that the window washer is pushing this brush up at a constant speed.

01:55 So that means that left and right our balance, up and down our balance.

01:58 So we can rewrite this.

02:00 Sorry, we forgot one force before i forget.

02:03 There's also friction opposing motion, so there's force of friction down.

02:09 So we can write two expressions...

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