imported>Patrick: Created page with 'We will consider the board and the diver as one object. Then the forces exerted on this system are the gravitational force on the diver (the magnitude is 60 N), $F_G$ …'

2011-07-20T20:06:13Z

Created page with 'We will consider the board and the diver as one object. Then the forces exerted on this system are the gravitational force on the diver (the magnitude is 60 N), <math>F_G</math> …'

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We will consider the board and the diver as one object. Then the forces exerted on this system are the gravitational force on the diver (the magnitude is 60 N), <math>F_G</math> and the forces exerted by the two supports, <math>F_1</math> and <math>F_2</math>. The force <math>F_1</math> acts on the system at the pivot, the force <math>F_2</math> acts at a distance 0.5 m from the pivot and the gravitational force acts at the distance of 3 m from the pivot. The diving board is in equilibrium and therefore

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

The diagram below shows the free body diagram and it also shows the force vectors tail-to-tail with the lever arm vectors. 
[[image:Helena_Stat_Equil_Ex_3_SolnA.png|TOP]] 

We will compute the torques. Note that the torque exerted by the force <math>F_1</math> is zero:

{| border="1" cellpadding="2" style="text-align:center"
|-
! Forces
! Direction
! Torque
|-
! <math>F_G</math>
| CW
| <math>\tau = -(3)(600)\sin{90^{\circ}} = -1800 Nm</math>
|-
! <math>F_2</math>
| CCW
| <math>\tau = (0.5) F_2 \sin{90^{\circ}} = 0.5 F_2</math>
|-
! <math>\Sigma \tau</math>
|
| 0
|}
 
Solving the equation

<math>F_2 = {1800 \over 0.5} = 3600 N</math>
 
The net force must be zero:

<math>F_1 + F_2 - 600 = 0</math>

<math>F_1 + 3600 - 600 = 0</math>

<math>F_1 = -3000 N</math>
 
The negative sign indicates that the force <math>F_1</math> points downward. It means that the diving board has to be "clamped" to the supporting pilon. The clamps that exert the downward force on the diving board.

Static Equilibrium EX 3 - Revision history

imported>Patrick: Created page with 'We will consider the board and the diver as one object. Then the forces exerted on this system are the gravitational force on the diver (the magnitude is 60 N), F_G …'

imported>Patrick: Created page with 'We will consider the board and the diver as one object. Then the forces exerted on this system are the gravitational force on the diver (the magnitude is 60 N), $F_G$ …'