NASA-Threads
Work and Mechanics
Lesson 16: Static Equilibrium
Equilibrium of Force Systems
When all of the forces that act on a stationary object are added up, the net force applied to
the body MUST be zero. This is a result of Newton’s 2nd Law:
𝚺𝑭 = 𝒎 ∙ 𝒂 = 𝟎
Writing this equation for the x-, y- and z-directions . . .
𝚺𝑭𝒙 = 𝟎
𝚺𝑭𝒚 = 𝟎
𝚺𝑭𝒛 = 𝟎
So, all of the x-components of the forces acting on an object must add up to zero, and
likewise for the y- and z-direction forces. This is a requirement for STATIC EQUILIBRIUM.
What does “static” mean? How about “equilibrium?”
1D Example
A child weighing 500N lies in a tire swing as shown. Use the principles discussed above to
find the tension in the rope.
NASA-Threads
Work and Mechanics
Lesson 16: Static Equilibrium
Example
A 100 lb weight is hung from cables as shown. Determine the forces in each cable.
Add up all of the y-components of the forces:
Add up all of the x-components of the forces:
Examine the solution:
NASA-Threads
Work and Mechanics
Lesson 16: Static Equilibrium
CLASS PROBLEM: A chair lift loaded with three passengers weighs 600 lbs.
Determine the forces in the cable to the left and right of the lift.
NOTE: You will end up with two equations and two unknowns when you write the
equilibrium equations.