1
00:00:04,010 --> 00:00:08,200
So now that we've combined
pulley A, string 2, platform,

2
00:00:08,200 --> 00:00:12,420
and washer as our system, we
can now address our question.

3
00:00:12,420 --> 00:00:16,170
If we measure the
acceleration of the person,

4
00:00:16,170 --> 00:00:19,810
what is the force that the
person pulls the rope down

5
00:00:19,810 --> 00:00:20,450
with?

6
00:00:20,450 --> 00:00:23,770
Well, of course, that will just
be the tension in the string.

7
00:00:23,770 --> 00:00:26,280
And with this simple
system, we can now

8
00:00:26,280 --> 00:00:30,760
apply Newton's second
law, F equals ma.

9
00:00:30,760 --> 00:00:33,880
But recall, we need
some directions.

10
00:00:33,880 --> 00:00:39,610
So suppose we expect that the
acceleration of the platform

11
00:00:39,610 --> 00:00:41,240
and person is up.

12
00:00:41,240 --> 00:00:46,490
So we'll choose a unit vector j
hat in the positive direction.

13
00:00:46,490 --> 00:00:50,350
And now the problem
becomes tension one,

14
00:00:50,350 --> 00:00:56,500
three different tensions,
3T1, and gravitational force

15
00:00:56,500 --> 00:01:01,570
minus mp plus mw times g.

16
00:01:01,570 --> 00:01:05,140
Now, what is the mass
that we have to consider?

17
00:01:05,140 --> 00:01:07,310
Again, what is the
mass of our system?

18
00:01:07,310 --> 00:01:08,750
Well, the platform
and the person,

19
00:01:08,750 --> 00:01:13,850
and we assume the pulley and
the string, too, were massless.

20
00:01:13,850 --> 00:01:18,906
So we have simply mp plus mw a.

21
00:01:18,906 --> 00:01:23,720
And so we can now solve for the
tension in the string, which

22
00:01:23,720 --> 00:01:33,140
is equal to mp plus mw
times g plus a divided by 3.

23
00:01:33,140 --> 00:01:39,050
And recall that this tension,
that the string is pulling,

24
00:01:39,050 --> 00:01:43,180
this is what we called
the force that the person

25
00:01:43,180 --> 00:01:45,210
[? of ?] the string
on the person.

26
00:01:45,210 --> 00:01:47,450
And by Newton's
third law, that's

27
00:01:47,450 --> 00:01:53,440
also, on the washer, that's
also the force that the washer

28
00:01:53,440 --> 00:01:56,259
applies to string 1.

29
00:01:56,259 --> 00:02:00,380
So this was our goal.

30
00:02:00,380 --> 00:02:04,930
It's the force that
the washer applies

31
00:02:04,930 --> 00:02:08,110
to string 1 by the third law.

32
00:02:08,110 --> 00:02:14,420
And so by thinking about
how to choose a system, what

33
00:02:14,420 --> 00:02:16,160
could be a very
complicated problem,

34
00:02:16,160 --> 00:02:20,684
with lots of equations,
is simply one equation.