1 00:00:00,420 --> 00:00:01,290 ‫Welcome back. 2 00:00:01,770 --> 00:00:05,530 ‫Let's now see the work for this system. 3 00:00:06,030 --> 00:00:14,220 ‫You have two forces here, force applied and force of gravity, so you have to compute work done by 4 00:00:14,220 --> 00:00:15,180 ‫both forces. 5 00:00:15,540 --> 00:00:18,630 ‫Let's first look at the Applied Force. 6 00:00:19,200 --> 00:00:24,540 ‫This is the applied force vector and the force of gravity vector is the following. 7 00:00:25,110 --> 00:00:34,150 ‫Its horizontal component is zero Newtons and its vertical component is minus five sine 30 degrees Newtons. 8 00:00:34,600 --> 00:00:35,250 ‫All right. 9 00:00:35,820 --> 00:00:38,070 ‫The displacement vector is the following. 10 00:00:38,340 --> 00:00:46,100 ‫The X component is 20 times cosine, 30 degrees, and the Y component is zero meters. 11 00:00:46,830 --> 00:00:47,240 ‫Right. 12 00:00:47,910 --> 00:00:57,660 ‫So the work done by the Applied Force is computed like this, the applied vector dart, the displacement 13 00:00:57,660 --> 00:01:03,750 ‫vector, which is this one times this one. 14 00:01:04,440 --> 00:01:13,800 ‫And then you add and I'm going to continue writing here, you add this component five sine thirty degrees 15 00:01:14,160 --> 00:01:18,540 ‫times, this component zero meters. 16 00:01:19,170 --> 00:01:28,710 ‫As a result, this term will be zero and you're left with five times 20, which is 100 times cosine, 17 00:01:28,710 --> 00:01:35,070 ‫30 degrees squared, and that will give you 75 joules. 18 00:01:35,580 --> 00:01:40,500 ‫So cosine 30 degrees squared equals zero point seventy five. 19 00:01:41,160 --> 00:01:43,940 ‫Now that's only work done by the Applied Force. 20 00:01:44,400 --> 00:01:46,910 ‫How about the work done by the force of gravity? 21 00:01:47,460 --> 00:01:51,300 ‫So you have the force of gravity vector times the displacement vector. 22 00:01:51,990 --> 00:02:00,660 ‫So you have zero times, 20 times cosine 30 degrees, which is this element times, this element here 23 00:02:01,080 --> 00:02:10,950 ‫plus minus five times sine thirty degrees, which is the summiteer times zero meters, which is this 24 00:02:10,950 --> 00:02:11,820 ‫element here. 25 00:02:12,300 --> 00:02:16,070 ‫And you can see that both terms are zero. 26 00:02:16,530 --> 00:02:20,250 ‫So work done by the force of gravity is zero joules. 27 00:02:20,790 --> 00:02:27,520 ‫And it makes sense because does the ball move in the direction of the force of gravity at all? 28 00:02:28,110 --> 00:02:28,860 ‫It doesn't. 29 00:02:29,250 --> 00:02:31,290 ‫It only moves horizontally. 30 00:02:31,470 --> 00:02:40,170 ‫But the force of gravity is vertical and work depends on the product of the force and the distance. 31 00:02:40,830 --> 00:02:47,850 ‫The ball must move in the direction of the force, at least a little bit in order for this force to 32 00:02:47,850 --> 00:02:48,870 ‫do some work. 33 00:02:49,470 --> 00:02:51,570 ‫If it doesn't, then there is no work. 34 00:02:52,140 --> 00:03:01,350 ‫And remember, the DOT product gives you a scalar and scalars are just numbers and so you can just add 35 00:03:01,350 --> 00:03:10,080 ‫them together, which means that the work total equals work done by the Applied Force plus work done 36 00:03:10,080 --> 00:03:11,640 ‫by the gravity force. 37 00:03:11,910 --> 00:03:19,140 ‫And since this one is zero, then you only have five joules like this. 38 00:03:19,860 --> 00:03:27,960 ‫And so that's why in physics you can just add energies because energies are scalar, they are not vectors, 39 00:03:28,290 --> 00:03:32,790 ‫energy doesn't have a direction, it's just a number, a quantity. 40 00:03:32,790 --> 00:03:35,390 ‫And that's why you can add them together like this. 41 00:03:36,150 --> 00:03:42,930 ‫So in this system, the only thing that contributes to total work is the horizontal component of the 42 00:03:42,930 --> 00:03:43,950 ‫applied force. 43 00:03:44,580 --> 00:03:46,740 ‫So that's all about the DOT product. 44 00:03:47,100 --> 00:03:50,890 ‫And now in the next video, we're going to start talking about the cross product. 45 00:03:51,390 --> 00:03:52,560 ‫Thank you very much. 46 00:03:52,560 --> 00:03:53,550 ‫And I'll see you there.