Overview

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Picture a rope going over a pulley. On one end hangs a block of twenty five kilograms, resting on the ground. On the other end, a monkey of just twenty kilograms. The monkey is lighter than the block. So can that monkey ever lift the block off the ground, just by climbing? Impossible, right? Hmm, hold that thought. We will settle it before the end. Questions on the laws of motion come up often in JEE, and this chapter, the unit problem bank, is where you test yourself on the whole unit. Today I will show you how to use it, and then we will solve two of its problems together. So, let's begin.

0:45How to use this chapter

So, let's open this chapter and see how to use it. Part A has twenty solved problems, at JEE Main level. Okay? And the course is very clear: attempt Part A as a forty minute test, after you finish Chapters one to eight. So first the chapters, then sit down with a clock, exactly like a real test. Right? Now, a quick one for you. Twenty problems, forty minutes. How much time can you give each problem? Forty over twenty; that is the division sign on screen. Two! About two minutes a problem, yes, exactly! Read it, spot the idea, solve it, and move on. Clear? And one rule for the whole chapter: take g, the acceleration due to gravity, as ten. On screen, m s to the power minus two means metres per second squared. Got it?

1:40Part B: JEE Advanced level

Now Part B: sixteen longer problems, at JEE Advanced level. And the course names the situations it covers. With me? First, free wedges. In the course problem, a block slides down the smooth face of a wedge, and the wedge itself is free to slide on a smooth floor. Two bodies moving at the same time. Okay? Then, strings that jerk tight. Two balls lie on a smooth table, joined by a slack string. One ball is sent off, and suddenly the string jerks tight. The course treats that jerk just like a perfectly inelastic collision. Right? Turntables and cones: a block on a turntable that slowly speeds up, and a particle going round on the smooth inside of a cone. Both are circular motion. Clear? And climbing on ropes. Remember our monkey? That is this kind of problem, and it will be our Example two. Got it?

2:36Part C and the unit test

Now, Part C checks the statements most often tested in true or false form, or in assertion reason form. Okay? Let me give you one statement from it. Capital A on screen stands for the assertion: a person in a freely falling lift feels weightless. Right? And capital R stands for the reason: gravity stops acting on a freely falling body. So tell me. Is the assertion true? And is the reason true? The assertion is true, yes! But the reason? Oh no, careful! It is false. Gravity still acts on the person. The floor simply exerts no normal force, capital N, because the person and the lift both fall with acceleration g. See, a true assertion can come with a false reason. So judge the two parts separately. With me? And at the very end of the chapter, the unit test: fourteen questions, with answers only, no worked solutions. Clear?

3:34Example 1: lift acceleration from the machine reading

Alright, here is an easy one from Part A to start with. Read it with me: a sixty kilogram man stands on a weighing machine in a lift, and the machine reads seven hundred and twenty newtons; capital N after the number is the newton. Find the lift's acceleration. Pause the video, and try it. Two minutes! Done? Okay, let's check. Seven hundred and twenty over sixty is twelve. So the acceleration is twelve metres per second squared, right? No, no, careful! Look at the figure: three lifts, each with a person standing on a weighing machine. The blue arrow, capital N, is the push of the machine, and that is what it reads. The green arrow, m g, is the weight, and the dark arrow, small a, is the lift's acceleration. Here N is seven hundred and twenty newtons, but the weight, m g, is sixty times ten, six hundred newtons. Okay? The man moves with the lift. In the ground frame, an inertial frame, the net upward force, N minus m g, equals m times a. So N equals m times, in brackets, g plus a, just like the left lift in the figure. Clear? Now put in the numbers: seven hundred and twenty equals sixty times, in brackets, ten plus a. Got it? Divide by sixty: ten plus a is twelve. The double arrow means therefore: a is two metres per second squared, and upwards, because N is more than m g. So that twelve was g plus a, not a alone. Very good!

5:13Example 2: monkey's least acceleration to lift the block

Now our puzzle from the start, as a Part B problem. Read it with me: a twenty kilogram monkey climbs a light rope. The rope passes over a smooth fixed pulley, and carries a twenty five kilogram block on its other end. With what least acceleration must the monkey climb to lift the block off the ground? Pause the video, and try it. Done? Okay, let's check. First, our puzzle. The monkey weighs two hundred newtons, and the block weighs two hundred and fifty. Lighter monkey, heavier block. So it can never lift the block, right? No, no, wait! The monkey does not just hang there; it climbs. Now, the rope is light and the pulley is smooth, so the tension, capital T, is the same all along the rope, on both sides. With me? So tell me, when does the block leave the ground? When the rope pulls it up harder than its weight, yes, exactly! So T must exceed twenty five times ten, two hundred and fifty newtons. Okay? Now the monkey. It pulls down on the rope, so by the third law, the rope pulls the monkey up, with the same tension T as on the block's side. Its weight, twenty times ten, two hundred newtons, acts down. So T minus two hundred equals twenty times a. Clear? For the least acceleration, T just reaches two hundred and fifty. Two hundred and fifty minus two hundred is fifty, so fifty equals twenty times a. And a is fifty over twenty: two point five metres per second squared, upwards. So yes, the lighter monkey can lift the heavier block! It just has to climb with an acceleration of more than two point five. Puzzle settled. Perfect!

6:57Quick revision: lift reading, climber tension, test plan

So, quick revision. Part A: twenty problems as a forty minute test, with g equal to ten. Part B is JEE Advanced level, and in Part C, judge the assertion and the reason separately. In a lift accelerating upwards, N equals m times, g plus a. And for a climber, T minus m g equals m a, and the block lifts once T is greater than its weight, that is the greater-than sign. Now start Part A, set your forty minute timer, and go. Then finish with the unit test at the end of the chapter. You can do this, I promise. All the best!