Equilibrium
When the net force on an object equals zero, that object is in equilibrium. At equilibrium, an object is
either at rest or moving with a constant velocity , but it is not accelerating.
You’ve heard of Newton’s first law, of course: an object maintains its velocity unless acted upon by a
net force. Well, an object in equilibrium is obeying Newton’s first law.
How to Solve Equilibrium Problems
We have a tried-and-true method. Follow it every time you see an equilibrium situation.
Draw a proper free-body diagram.
- Resolve force vectors into x - and y -components, if necessary.
- Write an expression for the vector sum of the left–right forces. Then write an expression for the
vector sum of the up–down forces. Set each of these expressions equal to zero. - Solve the resulting algebraic equations.
A Brief Interlude: UNITS!
Before we lose ourselves in the excitement of free-body diagrams, we need to pay tribute to the unit of
force: the newton. One N (as newtons are abbreviated) equals one kg·m/s^2 . We discuss why 1 newton
equals 1 kg·m/s^2 in a future chapter. For now, let it suffice that any force can be measured in newtons.
A Really Simple Equilibrium Problem
For those of you who prefer to splash your toes in the metaphorical swimming pool of physics before
getting all the way in, this section is for you. Look at this situation:
Two astronauts tug on opposite sides of a satellite. The first astronaut tugs to the left with a force of 30
N. With what force does the second astronaut tug in order to keep the satellite at rest?The solution to this problem is painfully obvious, but we’ll go through the steps just to be thorough.
Step 1 : Draw a proper free-body diagram.
We can skip Step 2 because these vectors already line up with each other, so they do not need to be