imported>Patrick: Created page with 'The rod is being studied. Three forces act on the rod: the tension in the wire $F_T$ ; the load $F_L$ and the support at the hinge $F$ . The wire i…'

2011-07-21T06:33:59Z

Created page with 'The rod is being studied. Three forces act on the rod: the tension in the wire <math>F_T</math>; the load <math>F_L</math> and the support at the hinge <math>F</math>. The wire i…'

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The rod is being studied. Three forces act on the rod: the tension in the wire <math>F_T</math>; the load <math>F_L</math> and the support at the hinge <math>F</math>. The wire is 60 cm long and it appears to be horizontal. It is attached in the middle of the rod. Thus, the wire, the wall and the rod form a right angle triangle with hypotenuse 1 m and one side of 60 cm. From this information, we can compute the angle between the rod and the wall:

<math>\cos{\theta} = {0.6 \over 1} = 0.6</math>

<math>\theta = 53^{\circ}</math>

The diagram below shows the forces and the lever arm for each of the forces. Note that the load acts 2.00 m from the pivot and the wire pulls at a distance 1 m from the pivot. The torque exerted by the support is equal to zero because it acts at the pivot. 
[[image:Helena_Stat_Equil_Ex_4_SolnA.png|TOP]] 

The rod is in equilibrium and so

<math>\Sigma F_x = 0</math>
<math>\Sigma F_y = 0</math>
<math>\Sigma \tau = 0</math>

We will first compute the torques:

{| border="1" cellpadding="2" style="text-align:center"
|-
! Force
! Direction
! Torque
|-
! <math>F_T</math>
| CW
| <math>\tau = -(1) F_T \sin{143^{\circ}} = -0.6 F_T</math>
|-
! <math>F_L</math>
| CCW
| <math>\tau = (2)(200)\sin{143^{\circ}} = 240 Nm</math>
|-
! <math>\Sigma \tau</math>
|
| 0
|}
 
Solving for <math>F_T</math>,

<math>F_T = {240 \over 0.6} = 400 N</math>
 
Then we will determine the components of the support at the pivot:

{| border="1" cellpadding="2" style="text-align:center"
|-
! Forces
! x-component
! y-component
|-
! <math>F_T</math>
| 400 N
| 0
|-
! <math>F_L</math>
| 0
| -200 N
|-
! <math>F</math>
| <math>-F_x</math>
| <math>F_y</math>
|-
! <math>\Sigma \vec{F}</math>
| 0
| 0
|}
 
Solving the two equations we find

<math>\vec{F} = 400 \hat{i} + 200 \hat{j}</math>

Static Equilibrium EX 4 - Revision history

imported>Patrick: Created page with 'The rod is being studied. Three forces act on the rod: the tension in the wire F_T; the load F_L and the support at the hinge F. The wire i…'

imported>Patrick: Created page with 'The rod is being studied. Three forces act on the rod: the tension in the wire $F_T$ ; the load $F_L$ and the support at the hinge $F$ . The wire i…'