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$\bullet$$\bullet$ A window washer pusheshis scrub brush up a verticalwindow at constant speed byapplying a force $\vec{F}$ as shown inFig. $5.69 .$ The brush weighs12.0 $\mathrm{N}$ and the coefficient ofkinetic friction is $\mu_{k}=0.150$Calculate (a) the magnitude ofthe force $\vec{F}$ and $(b)$ the normalforce exerted by the window onthe brush.

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

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question. Anyone states that a window washer pushes his scrub brush against vertical window at a constant speed by applying force F as shown in figure 5.69 which I represented here, the brush weighs 12 Newtons and the coefficient connect Friction is 0.15 jacket a the magnitude of the force and be the normal force exerted by the window on the brush. So question like this with benefits from a free body diagram. So if we look at this, free my diagram off the brush, you know that that was a four supplies in this direction here with above angles data, that means it's a force. If this is f this forces a why component jungle F y and a force into the, um, window f X, the normal force pushes away from it towards the window washer. And of course, it has a weight. W additionally, because because we're pushing the brush up, there'll be a friction for us acting opposite that direction. This is a fiction. Frictional force F little f. Okay, please. All the forces acting on her brush here. Our goal for Partney is we're gonna find the force exerted on the net Force f exerted on the you wouldn't know by the brush. Well, first you do look a my net forces in my Y direction. See what this will tell me? Because there's not moving a constant speed. The net acceleration zeros of the net force would also have to be zero means we have f Why is there a positive for us? You subtract off for two negatives of weight and friction equals zero and a little rearranging. So the F Y is given by the office tangle. Here's data and the Y component would be the sign of a forced. This is F I'm science, Tina, which equals the work plus a friction kinetic friction for us perches in UK times the normal. So they never looking my forces in my X direction which these air also zero I could find an expression for this I hope for didn't room before us. So I have my positive force to be normal and my negative if x force to be opposing that which equals zero. And so my normal for us equals f and because my wife was ability to sign death and my FX has B f Coast idea. Can I put this back into my Why term? So I have f science data isn't going to my weight. Plus you care after closing there looking at this now I know my foot. I don't in my four. So I'm trying to solve for that. I am data. I know weight and I know UK So I have all the terms I need to solve for the force. So I do a little rearranging f I can take out light terms for my f term when UK Costinha here just equal the weight. And so my net force I confined to be the weight divided by this angle. Term of science data minus from UK Coe's idea. And so here I get I have all my values here I can put them in and I can solve for this force to be 16.9 mins creating parties. What is the normal force exerted by the window on the brush? Well, we found that already in this term here, so are normal for us would just be 16.9 inches times co sign 53.1 degrees. Then we can solve for this distant to be 10.1. Do you know

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