ENSC2004 - Lecture 2

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ENSC2004 - Lecture 1
Condition for Equilibrium - Slides

2D Equilibrium

• When forces act in one 2D plane, it is known as a coplanar force system
• If forces all act through the same point, they are all concurrent
  e.g. all the forces below act on the same point $A$
  
  See: Definitions
• As seen in High School, static equilibrium is when the sum of all forces acting on a stationary particle are zero $\sum \vec{\text{F}}=\vec{0}$

Recall Newton’s First Law: A body will remain at rest, or continue moving with a constant velocity, unless acted upon by a net force

Simple Springs

• Spring force = spring constant $\times$ deformation of spring $\text{F}=\text{k}\times \text{s}$
  

Cables and Pulleys

• With a frictionless pulley and cable: ${\text{T}}_1={\text{T}}_2$
  i.e. the tension in both sides of a frictionless pully is constant
  
• Cable can support only a tension or “pulling” force, and this force always acts in the direction of the cable

Smooth Contact

• If an object rests on a smooth surface, then the surface will exert a force on the object that is normal to the surface at the point of contact

For problem solving systems of equilibrium, it is recommended to always draw out a free body diagram and then use your knowledge of vector addition to solve for each force

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Moments - Slides

Moment of a Force

• A force may cause a body to move in the direction of its application
  • It may also cause a body to rotate about an axis
• The moment of a force about a point provides a measure of its tendency to cause rotation about that point
  • Also known as torque
    • See also: Torque
• We can notate a moment of force $\text{F}$ around point $\text{O}$ as ${\text{M}}_{\text{O}}$ ${\text{M}}_{\text{O}}=\text{F}\text{d}$
  • $\text{d}$ is the perpendicular distant from point $\text{O}$ to the line of action of the force (i.e. the line of direction in which the force acts)
• Torque is given either a clockwise or counter-clockwise direction in 2D
  • Counter-clockwise is considered positive

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ENSC2004 - Lecture 3