1 00:00:00,550 --> 00:00:07,390 Let us look at the principle of impulse and momentum now to do this, we need to recap just quickly 2 00:00:07,390 --> 00:00:13,870 the principle of work and energy and see how that is different from the principle of impulse and momentum. 3 00:00:14,560 --> 00:00:21,630 So the principle of work and energy, we could solve problems involving forces, positions and speed. 4 00:00:22,330 --> 00:00:31,660 So to get from velocity one to velocity, too, we considered the work done on a body to give it velocity 5 00:00:31,660 --> 00:00:36,780 to, and that work was a force that worked in over a certain distance. 6 00:00:37,480 --> 00:00:43,860 Now, with Impulse, we are going to look at problems involving forces, time and velocity. 7 00:00:44,200 --> 00:00:51,010 So to get from velocity one to velocity too, we apply a certain impulse, which is a force that works 8 00:00:51,010 --> 00:00:52,720 in over a certain time. 9 00:00:53,500 --> 00:00:57,010 So work is a force that works in over a certain distance. 10 00:00:57,520 --> 00:01:00,900 Impulse is a force that works over a certain time. 11 00:01:01,780 --> 00:01:04,240 So that is more or less the difference between the two. 12 00:01:04,750 --> 00:01:11,350 And a force can create an impulse on a particle without doing work on that particle. 13 00:01:11,360 --> 00:01:17,620 So even if the particle or the body is not moving, they can still be an impulse, whereas with work 14 00:01:17,620 --> 00:01:20,450 there is always displacement involved. 15 00:01:21,130 --> 00:01:28,420 So, as I've said, an impulse is basically a force multiplied by the time in which that force works 16 00:01:28,420 --> 00:01:28,770 in. 17 00:01:29,200 --> 00:01:32,340 So let us first look at the case for constant force. 18 00:01:33,640 --> 00:01:39,380 We know that according to Newton's second law, F is equal to M multiplied by eight. 19 00:01:39,880 --> 00:01:44,410 So if I multiply both sides with T, I get on the left and side. 20 00:01:44,410 --> 00:01:47,080 If T is equal to M80. 21 00:01:48,420 --> 00:01:59,010 Now, according to our equations for Motion, V1 is V0 plus 80, so therefore 80 is V1 minus V0. 22 00:01:59,040 --> 00:02:10,500 So I can substitute that in for 80 and then we get if this is equal to M V1 minus V0 and F.T. Force 23 00:02:10,500 --> 00:02:13,470 multiplied by the time that is called the impulse. 24 00:02:13,950 --> 00:02:22,800 And so the impulse is equal to M.V. one minus in V zero or you could say in two minus M.V. one. 25 00:02:23,580 --> 00:02:30,090 But it comes down to the fact that it is an initial velocity and a final velocity. 26 00:02:31,130 --> 00:02:41,090 Before and after the impulse, so for a variable force, we need to consider the time period for each 27 00:02:41,090 --> 00:02:42,550 magnitude of the force. 28 00:02:42,560 --> 00:02:46,280 If there's a variable force that varies in time, we need to integrate. 29 00:02:47,230 --> 00:02:54,970 So we say the some of the forces and I, I make this force a vector, it's got direction is equal to 30 00:02:55,000 --> 00:02:58,300 M.A that is equal to MDVIP. 31 00:02:59,170 --> 00:03:06,490 And if we multiply both sides by DETI, we get if it is in the V now, we can integrate. 32 00:03:06,520 --> 00:03:08,800 Now remember, this force is variable. 33 00:03:08,800 --> 00:03:14,860 That is why we need to integrate between our starting time to one and our ending time two. 34 00:03:15,280 --> 00:03:24,460 So the integral of FTD between T1 and T2 is equal to the integral between velocity and velocity of MTV 35 00:03:24,790 --> 00:03:27,320 exactly the same as what we did in the previous slide. 36 00:03:27,340 --> 00:03:35,320 This is just with a variable force and therefore I is equal to M V to minus V1. 37 00:03:35,320 --> 00:03:40,730 No I r impulse that is the integral between T one and two of FTT. 38 00:03:41,590 --> 00:03:47,980 So once again it's just multiplying the force with the time and because the forces variable we're going 39 00:03:47,980 --> 00:03:48,570 to integrate. 40 00:03:48,580 --> 00:03:53,800 So we're going to sum all these different little components of the force multiplied by the time. 41 00:03:54,640 --> 00:04:03,880 And so the impulse is equal to M.V. to minus one and we can rearrange that to say, M.V. one plus the 42 00:04:03,880 --> 00:04:08,730 impulse is M.V. two, and that is our principle of impulse and momentum. 43 00:04:08,740 --> 00:04:12,160 So you can see that you have an M.V. one or a momentum. 44 00:04:13,270 --> 00:04:19,390 If you add to that an impulse, you're going to get a second new momentum, M.V. two. 45 00:04:20,350 --> 00:04:27,580 And so because impulse is force multiplied by time, if you plot the force as a function of time, the 46 00:04:27,580 --> 00:04:32,070 area under the force time curve, that will give you your impulse. 47 00:04:32,380 --> 00:04:38,530 So the larger the force, the larger the impulse, the larger the time, the larger the impulse, because 48 00:04:38,530 --> 00:04:41,020 it's the area under the force time curve. 49 00:04:41,320 --> 00:04:43,630 Now, what I've drawn here is a variable force. 50 00:04:43,840 --> 00:04:45,430 That is why we need to integrate. 51 00:04:45,430 --> 00:04:50,980 If it was a constant force, it would have just been a straight line and we could just take if multiplied 52 00:04:50,980 --> 00:04:55,700 by t to get the area under the curve, as we've done in the previous slide. 53 00:04:56,200 --> 00:04:58,480 So it's the same principle. 54 00:04:58,780 --> 00:05:04,660 But you should just remember for constant force, you can just take if multiplied by T and for a variable 55 00:05:04,660 --> 00:05:06,220 force, you'll have to integrate. 56 00:05:06,970 --> 00:05:12,060 Now let us illustrate impulse and momentum in two in three different ways, actually. 57 00:05:12,490 --> 00:05:18,530 So the equation says M.V. one plus the impulse is equal to M.V. two. 58 00:05:19,510 --> 00:05:26,470 Now I have written this in vector form because the velocities and the impulses can be broken down in 59 00:05:26,470 --> 00:05:30,070 the three Briem primary directions. 60 00:05:31,300 --> 00:05:39,460 We can draw it as a vector diagram, so if M.V. one is to the right and the top and we add an impulse 61 00:05:39,460 --> 00:05:44,770 that goes to the top and to the left, then M.V. two will be to the left and the top. 62 00:05:44,770 --> 00:05:53,080 So M.V. one plus the impulse will give you M.V. to we can draw in terms of using balls. 63 00:05:53,110 --> 00:06:02,020 So if you have a ball drawn here by a blue circle with a momentum in one going to the right and the 64 00:06:02,020 --> 00:06:09,220 top, plus an impulse on the ball that goes to the left and the top, that would give you a velocity 65 00:06:09,640 --> 00:06:13,150 multiplied by a mass going to the left and the top. 66 00:06:14,230 --> 00:06:16,720 So M.V., that is momentum. 67 00:06:16,720 --> 00:06:20,420 And you'll recognize this also from from school. 68 00:06:21,520 --> 00:06:27,970 So let us break down M.V. one plus I'm equals M.V. two into its different components. 69 00:06:27,970 --> 00:06:29,790 So predominant as a vector. 70 00:06:29,800 --> 00:06:32,890 Let's break it down into its X, Y and Z components. 71 00:06:33,910 --> 00:06:38,290 So if we expand that equation, it'll say M.V. one in the X direction. 72 00:06:38,290 --> 00:06:41,960 Plus the impulse in the X direction is in between the X direction. 73 00:06:42,490 --> 00:06:48,940 Similarly, in the one in the Y direction, plus the impulse in the Y direction is M.V. two in the Y 74 00:06:48,940 --> 00:06:49,580 direction. 75 00:06:50,020 --> 00:06:53,170 Similarly, M.V. one in the Z direction. 76 00:06:53,170 --> 00:06:57,580 Plus the impulse in the direction is M.V. two in this direction. 77 00:06:58,810 --> 00:07:04,360 So the impulse has components and we can find the magnitude. 78 00:07:04,360 --> 00:07:06,150 How large is this impulse? 79 00:07:06,670 --> 00:07:14,490 We get that by taking the square root of the sum of the squares of the different components of the impulse. 80 00:07:14,890 --> 00:07:20,890 So the magnitude of the impulse is a square root of the impulse in the X direction squared, plus the 81 00:07:20,890 --> 00:07:26,030 impulse in the Y direction squared, plus the impulse in the in the Z direction squared. 82 00:07:27,010 --> 00:07:33,860 So this is the theory you need to know to apply the principle of impulse and momentum on a basic problem. 83 00:07:34,390 --> 00:07:37,300 So in the next video, we'll have a look at an example.