1
00:00:00,390 --> 00:00:02,190
‫Let's take another case now.

2
00:00:02,880 --> 00:00:13,020
‫Again, you have the ball and the same force is acting on the ball diagonally at the angle of 30 degrees

3
00:00:13,440 --> 00:00:21,480
‫and your ball travels along that diagonal, 20 meters like you see here.

4
00:00:22,050 --> 00:00:27,090
‫The force applied was five Newtons diagonally.

5
00:00:27,580 --> 00:00:32,710
‫And the absolute values here mean that it is the magnitude of the vector.

6
00:00:33,280 --> 00:00:40,830
‫Remember, if you have a vector, let's say A and B and you want to compute its magnitude, then it

7
00:00:40,830 --> 00:00:46,140
‫would be like this square root, A squared plus B squared.

8
00:00:46,770 --> 00:00:50,510
‫And essentially this would be your A component.

9
00:00:51,150 --> 00:00:54,060
‫This would be your B component.

10
00:00:54,660 --> 00:00:59,490
‫And the Green Arrow here is the magnitude of this vector.

11
00:00:59,940 --> 00:01:01,530
‫It's the length of this arrow.

12
00:01:02,070 --> 00:01:06,090
‫Now, we can also write this force vector like this.

13
00:01:06,660 --> 00:01:09,170
‫We can use the vector form.

14
00:01:09,690 --> 00:01:17,190
‫And so the X component of this force would be five Newton's times cosine.

15
00:01:17,370 --> 00:01:19,050
‫Thirty degrees.

16
00:01:19,350 --> 00:01:19,830
‫Right.

17
00:01:20,280 --> 00:01:28,650
‫You would get this component then and the Y component would be five times sine thirty degrees.

18
00:01:29,010 --> 00:01:36,180
‫And so you would get this component then in the same thing with the displacement vector, the X component

19
00:01:36,180 --> 00:01:47,400
‫would be 20 times cosine, 30 degrees in the Y component would be 20 times sine 30 degrees and the units

20
00:01:47,400 --> 00:01:52,950
‫for the force vector would be Newton's and for the displacement vector meters.

21
00:01:53,430 --> 00:01:58,890
‫So work here would be five times cosine.

22
00:01:58,890 --> 00:02:10,440
‫Thirty degrees, which is the force X component times 20 times cosine, 30 degrees, which is this.

23
00:02:11,040 --> 00:02:20,460
‫Plus I'm going to continue here five times sine thirty degrees, which is this one times.

24
00:02:21,000 --> 00:02:25,050
‫Twenty times sine thirty degrees which is this one.

25
00:02:25,710 --> 00:02:29,370
‫Then that means that you will get this.

26
00:02:29,790 --> 00:02:39,960
‫The first term would be one hundred five times, 20 times cosine, 30 degrees squared plus again you

27
00:02:39,960 --> 00:02:41,400
‫would have five times twenty.

28
00:02:41,410 --> 00:02:52,470
‫So one hundred and sine thirty degrees squared you can factor out one hundred and inside the parentheses

29
00:02:52,860 --> 00:03:00,360
‫you would have cosine 30 degrees squared plus sine thirty degrees squared.

30
00:03:00,990 --> 00:03:14,220
‫And now there is a trigonometric identity that says that cosine alpha squared plus sine alpha squared

31
00:03:14,640 --> 00:03:17,640
‫were both alphas are the same angles.

32
00:03:17,820 --> 00:03:18,090
‫Right.

33
00:03:18,120 --> 00:03:19,040
‫It's the same angle.

34
00:03:19,500 --> 00:03:24,180
‫So when you have something like this then that will equal one.

35
00:03:24,690 --> 00:03:27,390
‫And that's a very famous trigonometric identity.

36
00:03:28,020 --> 00:03:33,530
‫And that means that here this thing here will be one.

37
00:03:34,440 --> 00:03:37,770
‫So you are left with and I'm going to continue here.

38
00:03:38,520 --> 00:03:46,080
‫You are left with one hundred, which is this one times one, which is this one here.

39
00:03:46,410 --> 00:03:52,200
‫And so you have one hundred jewels of work done.

40
00:03:53,100 --> 00:04:04,080
‫By this force, because only this force moved this ball from here to here over the distance of 20 meters.