More about Friction

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Everyone calls friction the enemy of motion, right? It slows things down and wastes energy. So imagine a floor with no friction at all, smoother than the smoothest ice. You stand in the middle of it, and you want to walk to the door. Can you even take one step? Keep your answer in mind; we will settle it in a minute. Today: friction as a helper, the work friction does, and how high a block can sit inside a rough bowl. These ideas come up often in JEE, so let's begin.

0:37Friction as a helper

So, let's settle our puzzle. Watch what your foot does when you take a step. It pushes the ground backwards, okay? Now, friction opposes motion; everybody knows that. You are moving forwards, so friction on your foot must act backwards, right? Think again. Which way does it really act? No, no, careful! It acts forwards. Your foot tends to slip backwards on the ground, and friction opposes that slipping, so the ground pushes your foot forwards. And since the foot does not actually slide, this is static friction. So friction opposes slipping between the two surfaces, not your motion. With me? Same story for a car. The driving wheels, the ones the engine turns, push the road backwards, so the road pushes them forwards. So on the driving wheels of an accelerating car, friction acts forwards too. Clear? And now our puzzle is settled. On a floor with no friction, your foot just slides back, and nothing pushes you forwards. You could not start walking, and a car could not start either. So friction is not only the enemy; very often it is the helper. Got it?

1:48Rolling friction and lubricants

Now, a quick one. You have to move a heavy box across the room. Which is easier: drag it along the floor, or put it on wheels and roll it? Roll it, of course! When a wheel rolls on a surface, the friction is called rolling friction, and it is much smaller than sliding friction. The double less-than sign on screen means much smaller than. Okay? That is exactly why machines use wheels, and ball bearings, where small balls roll between the moving parts instead of sliding. Right? And where parts must slide, we use lubricants. Lubricants reduce friction, so less energy is wasted, and machines work more efficiently.

2:27Work done by kinetic friction

Clear? Now, the work that friction does. Take a block sliding on a rough surface. Kinetic friction on it is mu times N, where mu, this Greek letter, is the coefficient of kinetic friction, and capital N is the normal reaction, the push of the surface. And this friction acts against the motion, okay? The block moves forwards, and friction pulls it backwards. So is the work done by friction positive, or negative? Negative, exactly! The force is opposite to the displacement. So if the block slides a distance s, the work, capital W, equals minus mu N s. Right? Now, a special case. On a level floor, with no other force pushing up or down, N equals m g, the weight. So W equals minus mu m g s. But remember the condition: a level floor, and no other vertical force. With me? And this energy does not just vanish. Friction turns the block's kinetic energy into heat. Got it?

3:32Resting on a rough curved surface

Now the last idea. Recall rough inclines from the last lesson. On an incline at angle theta, this Greek letter, a block stays at rest by itself if tan theta is less than or equal to mu; that is this sign, with the line under it. Here mu is the static coefficient, because the block is at rest. Okay? But now the surface is curved, like the inside of a bowl. The steepness changes from point to point, so there is no single angle theta. So what plays the role of tan theta now? The slope of the tangent, yes! Here y of x is the height of the surface at the sideways position x. Zoom in close to any point, and the curve looks like a tiny straight incline. Its slope is d y over d x, the derivative of y with respect to x, and that is exactly tan theta at that point. Right? So the block rests at a point where the modulus of d y over d x is less than or equal to mu. The two straight bars are the modulus: they keep the size of the slope and drop its sign. We need them because on the other side of the bowl the slope is negative, and the block can slip that way too. Clear?

4:43Example 1: work done by friction on a sliding block

Alright, example one, an easy one. Read it with me: a two kilogram block slides five metres on a floor, with mu k equal to zero point three; the small k below mu means kinetic. Find the work done by friction. Pause the video, and try it first. Done? Okay, let's check. The floor is level, and we take g as ten metres per second squared; that is the m s to the minus two you see on screen. So N equals m g: two times ten, which is twenty newtons. The upright N after the number is the newton, the unit of force, okay? Now the formula: W equals minus mu k, times N, times s. That is minus zero point three, times twenty, times five. With me? Zero point three times twenty is six, and six times five is thirty. So the answer is thirty joules, right? Oh no, careful! You dropped the minus sign. Friction acts against the motion, so its work is negative: minus thirty joules. The capital J is the joule, the unit of work. Those thirty joules of kinetic energy have turned into heat. Got it?

5:57Example 2: greatest height a block can rest in a rough bowl

Now a harder one. Read it with me: a small block rests on the inside of a rough bowl, whose cross-section is y equals x squared over two, with mu equal to zero point five. The little two up on x means squared. Find the greatest height at which the block can stay at rest. Pause the video and try it. Hint: start with the slope. Done? Okay, let's check. Step one, the slope. Here y equals x squared over two, so d y over d x is just x. At the bottom, the slope is zero, and the bowl gets steeper as you go out. With me? Step two, the condition for rest. The modulus of the slope, that is the modulus of x, must be at most mu, zero point five. So the block can stay anywhere between x equal to minus zero point five metres and plus zero point five metres. Beyond that, the bowl is too steep. Okay? So the greatest height is zero point five metres, right? No, no, wait! Zero point five metres is x, the sideways distance from the centre, not the height. The height is y. So put x equal to zero point five into the curve: zero point five squared is zero point two five, and over two, that gives zero point one two five metres. That's it! The greatest height is zero point one two five metres. Perfect!

7:24Quick revision: walking, work by friction, curved surfaces

So, quick revision. Friction is a helper: static friction pushes your feet, and the driving wheels of an accelerating car, forwards. Kinetic friction does negative work, minus mu N s, and turns kinetic energy into heat. And on a rough curved surface, a block rests where the modulus of d y over d x is at most mu. Now go and try the practice problems on this page. All the best!