Force and Equilibrium

Forces in Equilibrium

Grade 9

• And the Horizontal components together F1x + F2x = Rx

• And the Vertical components together F1y + F2y = Ry

• Calculate R =

   $\sqrt{Rx^2\ +\ Ry^2}$  

• Find  $\Theta=\tan^{-1}\left(\frac{\ Ry}{Rx}\right)$  

• Now Calculate E = R in the opposite direction.

Learning objectives

• Define conditions of equilibrium for multiple forces acting in 2 dimensions

• Determine the equilibrant of two non-coplanar forces.

• Calculate unknown forces for objects in static or dynamic equilibrium

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Vocabulary

• Resultant

• Vector resolution

• Equilibrium

• Equilibrant

Brains in gear

• How can you find the equilibrant of two forces?

  
  

How could you find a third force that, when added to the other two, would add up to zero and put the object in equilibrium?

Steps to find the equilibrant of two or more forces

• Draw a vector diagram

• Find the horizontal component of the first force. F1x = F1 cos $\theta$  

• Find the vertical component of the first force. F1 y = F1 sin  $\theta$  

• Similarly find the components of the second force.

• And the vertical components F1y + F1y = Ry

Example

A large scoreboard is suspended from the ceiling of a sports arena by 10 strong cables. Six of the cables make an angle of 8.0° with the vertical while the other four make an angle of 10.0°. If the tension in each cable is 1300.0 N, what is the scoreboard’s mass?

Multiple Choice

What is the term used to describe a force that equals the sum of two or more forces?

• Resultant

• Equilibrant

• Tension

• Friction