# Math Help - Mechanics new question just need a slight help

1. ## Mechanics new question just need a slight help

i couldnt solve the last part where u have to find the resultant i know that the forumla to find the resultant but yet cant find it. I know that horizantal forces is 192cos50 but what would be the sum of vertical forces help

2. ## Re: Mechanics new question just need a slight help

$T_1 \cos(40) = T_2 \cos(50)$

$T_1 = \frac{T_2 \cos(50)}{\cos(40)}$

$T_1 \sin(40) + T_2 \sin(50) + 150 = 400$

$T_1 \sin(40) + T_2 \sin(50) = 250$

$\frac{T_2 \cos(50)\sin(40)}{\cos(40)} + T_2 \sin(50) = 250$

$T_2\left[\cos(50)\tan(40) + \sin(50)] = 250$

$T_2 = 192 \, N$

$T_1 = 161 \, N$

forces on the pulley in the x-direction (leftward) ...

$T_2 \cos(50)$

forces on the pulley in the y-direction (downward) ...

$T_2 \sin(50) + T_2$

Resolving forces acting on the pulley ...

$|F| = \sqrt{[T_2 \cos(50)]^2 + [T_2 \sin(50) + T_2]^2} = 360 \, N$

$\theta = \arctan\left[\frac{ T_2 \sin(50) + T_2}{T_2 \cos(50)}\right] = 70^\circ$ relative to the horizontal ... same as $20^\circ$ relative to the vertical

3. ## Re: Mechanics new question just need a slight help

u deserve a million thanks well i just wanted to know what would be the vertical forces well thanks anyway u did a too much writing

4. ## Re: Mechanics new question just need a slight help

Originally Posted by abdulrehmanshah
u deserve a million thanks well i just wanted to know what would be the vertical forces well thanks anyway u did a too much writing
Note that I have to do the problem from the start so that I understand how the entire problem develops.

It's like coming into a movie after it has been running a while ... you really do not understand what is going on.