Lessons â€ē 2 Mechanics â€ē 2.3 ForcesPrevious lessonNext lesson

2.3.2 Forces in Equilibrium

By the end of this lesson you can:

  • Explain the condition for translational equilibrium
  • Resolve forces into components to find an unknown force
  • Solve problems involving tension and balanced forces
Find your course: NSW Year 11: Forces and motionNSW Year 12QLD Unit 2: Linear motion and forceVIC Unit 2: MotionAP Physics 1: Unit 2IB: A.2 Forces and momentum
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Learn the idea: a short explanation, then a check.

When two or more forces act on an object such that their combined net force is zero, the object experiences no acceleration and is said to be in mechanical equilibrium.

This is a direct application of Newton's First Law of Motion, which states that an object will maintain a constant velocity (or remain at rest) unless acted upon by a non-zero net force.

Because the net force is zero (∑ F = 0), these scenarios can be analyzed vectorially. By resolving force vectors into horizontal and vertical components, we can set up equations where the opposing forces balance each other out:

  • Horizontal Equilibrium: ∑ Fx = 0
  • Vertical Equilibrium: ∑ Fy = 0


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​Using weights and pulleys, a situation can be in equilibrium, where there is no net force.
This video looks at the situation and helps you mathematically analyse the situation
 
📝Practise
Worked examples first, then problems to try, then worksheets.
Sample Problem
We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.
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  1. Examine the diagram below.  Calculate the tensions in the ropes. (885 N, 1085 N)
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Here is a worksheet on equilibrium situations (includes answers)
🕹ī¸Explore
Test your predictions in a simulation.

Interactive 1

Interactive 2

The following interactive, from Walter Fendt, is a useful to explore and assess your understanding of force in equilibrium.

Set the masses and then calculate the angles and see if you agree with the angles provided