Part C: Concept Checks

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle before we start. You are standing on a weighing machine inside a lift, and the lift starts falling freely. The machine reads zero. You feel completely weightless. So tell me, has gravity switched off? Most students say yes. Hold on to your answer. Today we do quick concept checks on the laws of motion: true or false, and assertion reason. Such one line questions do appear in JEE, and they test whether you really understand Newton's laws. So, let's begin.

0:35Assertion and Reason: three checks

So, let's settle the puzzle with an assertion reason question. For every such question, make three checks, in order. Is the assertion true? Is the reason true? And does the reason explain the assertion? Okay? Here is the assertion: a person in a freely falling lift feels weightless. Check one: that is exactly our puzzle, so true. Right? Check two. The reason: gravity stops acting on a freely falling body. Is this true? No, no, careful! False! This is the trap. Gravity still acts; it never switches off. What becomes zero is capital N, the normal force, the push of the floor on you. And the weighing machine reads this normal force, not gravity. With me? And why does the floor stop pushing? Because you and the floor both fall with the same acceleration, small g, the acceleration due to gravity. So you never press on it. Clear? So, assertion true, reason false. And check three is automatic: a false reason explains nothing. Puzzle solved: gravity never left; only the reading became zero. Got it?

1:47Action and reaction: what is the same?

Next, Newton's third law. Look at the figure: a book on a table. Capital N, the blue arrow, is the table's push on the book, and the arrow labelled book on table is the book's push back on the table. Action and reaction. Now, which are the same for this pair: the magnitudes, the kind of force, the bodies they act on, or the accelerations? The magnitudes, yes, always equal. And the kind of force is the same: here, both are contact forces. Okay? So the two forces are equal. Then the accelerations must be equal too, right? No, no, wait! Look where the arrows act. One acts on the book, the other on the table: different bodies! And different bodies generally have different masses and other forces on them. The double arrow on screen means so: the accelerations generally differ. So the answer: only the magnitudes and the kind of force. Got it? One more trap here. Capital W, the green arrow, is the earth's pull on the book, its weight. N equals W, but they are not an action reaction pair! Both act on the same book. As the notes beside the figure say, the reaction to W is the book's pull on the earth. Right?

3:03Friction is not automatic

Alright, now friction. Ignore the figure for a moment. Take a block resting on a horizontal floor, and nothing pushes it sideways. Is there any friction on it? No friction at all! Friction opposes relative motion, or the tendency of relative motion. Here the block has no tendency to slide, so there is nothing to oppose. Friction is not automatic, okay? Now the left picture: a block at rest on a rough incline of angle theta, the Greek letter. It tends to slide down, so friction, small f, the orange arrow, acts up the slope. Capital N, in blue, is the normal force; m g, in green, is the weight. On the right, the block moves up with velocity v, so friction acts down the slope. Clear? Now, a check that comes up in assertion reason form. N and f together make the incline's total force, the contact force. Apart from it, only m g acts on the block. So which way must it point? Straight up, exactly! Not perpendicular to the slope. The block is at rest, so the net force is zero, and the incline's force must cancel m g, which points straight down. So in assertion reason form: the assertion, that this force points vertically up, is true; the reason, that the net force is zero, is true; and the reason explains it. Beautiful, isn't it?

4:26Example 1: apparent weight in a lift going up but slowing

Example one, an easy one. Here, a lift is moving up, but slowing down. Is a passenger's apparent weight more or less than the true weight? Apparent weight is the machine's reading, the normal force. In the figure, three lifts: N in blue, the weight m g in green, the lift's acceleration small a, and each lift's reading below it. Pause the video, and try it first. Done? Okay, let's check. The lift is going up, so the passenger feels heavier, right? Oh no, careful! That is the trap. Only the direction of the acceleration matters, not the direction of motion. The velocity points up, but it is getting smaller. So the acceleration vector, a with an arrow on top, points down. Okay? So this lift is like the one on the right of the figure, accelerating down. In the ground frame, N equals m times, in brackets, g minus a, and the less than sign says it is below m g. Right? So the apparent weight is less than the true weight: the passenger feels lighter. And as the caption says, in free fall the machine reads zero: our weightless puzzle again! See how it connects?

5:43Example 2: true or false on friction and banked roads

Now a harder one, JEE level: true or false. Statement one: friction always opposes the motion of a body. Statement two: static friction can do work on a body in the ground frame, that is, as seen from the ground. Statement three: at its design speed, a car on a banked road presses on it with less than its weight. Pause and try. Hint: think of a box on a truck that speeds up. Done? Okay, let's check. Statement one: friction opposes motion. We all learnt that, so it is true, right? Oh no, careful! This is the JEE trap. Friction opposes relative motion between the surfaces, or the tendency of it, not motion itself. The same rule we used for the block on the level floor. With me? Take a box on the floor of a truck that speeds up. Relative to the floor, the box tends to slide backwards, so friction acts forwards and carries it along. Friction along the motion! So statement one is false. Statement two. Static friction acts when there is no slipping. Can such a force do work on a body, as seen from the ground? Yes, it can! Same box. It does not slip, so the friction on it is static. But seen from the ground, the box moves forwards, along the friction, so friction does work on it. Statement two is true. Got it? Statement three. The design speed is the speed at which no friction is needed. By the third law, the car presses on the road with the same N that the road exerts on it. So, is N more or less than m g? More! With no friction, only N and m g act. The car goes round a horizontal circle, so there is no vertical acceleration, and vertically, N times cos theta balances m g; theta is the banking angle, and cos is the cosine. So N equals m g over cos theta. Cos theta is less than one, so N is greater than m g, as the greater than sign shows. False! So the answer: false, true, false. Two traps in one question!

7:59Quick revision: free fall, action-reaction, friction

So, quick revision. Gravity never switches off; free fall only makes the normal force zero. Action and reaction are equal and opposite, and of the same kind, but act on different bodies. Friction opposes relative motion, and in a lift, use the direction of the acceleration, never the direction of motion. Now go and try the practice problems on this page. Make your three checks every time, and these traps will not catch you. All the best!