Page 143 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 11

Equilibrium

TRANSLATIONAL EQUILIBRIUM

A body is in translational equilibrium when no net force acts on it. Such a body is not accelerated, and it remains
either at rest or in motion at constant velocity along a straight line, whichever its initial state was.
A body in translational equilibrium may have forces acting on it, but they must be such that their vector sum
is zero. Thus the condition for the translational equilibrium of a body may be written

F = 0

where (as before) the symbol (Greek capital letter sigma) means “sum of” and F refers to the various forces
that act on the body.
The procedure for working out a problem that involves translational equilibrium has three steps:

1. Draw a diagram of the forces that act on the body. As mentioned in Chapter 5, this is called a free-body
diagram.
2. Choose a set of coordinate axes and resolve the various forces into their components along these axes.
3. Set the sum of the force components along each axis equal to zero so that

Sum of x force components = F x = 0

Sum of y force components = F y = 0
Sum of z force components = F z = 0

In this way the vector equation F = 0 is replaced by three scalar equations. Then solve the resulting
equations for the unknown quantities.

A proper choice of directions for the axes often simplifies the calculations. When all the forces lie in a plane,
for instance, the coordinate system can be chosen so that the x and y axes lie in the plane; then the two equations
F x = 0 and F y = 0 are enough to express the condition for translational equilibrium.

SOLVED PROBLEM 11.1
◦
A 100-N box is suspended from two ropes that each make an angle of 40 with the vertical. Find the
tension in each rope.
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