00:01
Hello, here we have to solve the following problem.
00:04
Weight of 250 newton is suspended and we have to find tensions in the cables.
00:12
Let's start from situation a.
00:15
Here we have to find t a, c b and tc.
00:20
Let's start with a cable to which the weight is hold.
00:26
So here this cable, this weight experience, this block experience is gravity.
00:31
Downwards and tension tc up therefore tc equals to gravity acting on the block which is 250 newtons now let's look at a and b let's sketch t b and t a and here on the one hand tc equals to t b or t a on the other hand, t .a.
01:12
Cosine 30 is tb.
01:16
Cosine 45.
01:19
So now we can rearrange these two equations in the way that from the first we express t .a.
01:24
Sign of 30.
01:26
T .a.
01:26
Sign of 30 is t .c.
01:30
Minus t .b.
01:33
Sign of 45.
01:35
And now we can combine these two equations into one.
01:41
Tangent of 30 is t .c.
01:47
Minus t .b.
01:48
Over sine of 45 divided by t b cosine of 45 and that is tc over t b cosine 5 minus tangent 45 so therefore tc over t b cosine of 45 equals to sum of these two tangents of 30 and 45 therefore t b is tc over cosine 45 times tangent of 30 plus tangent of 45.
02:32
Let's calculate it.
02:49
Let's complete this calculation.
03:33
That is 224 newtons.
03:37
And now we can calculate t .a.
03:40
T .a is tb cosine of 45 over cosine of 30.
04:00
Let's calculate it.
04:08
That is 183 newtons...