Equilibrium Physics Example 3

Follow the full solution, then compare it with the other examples linked below.

medium

An object is in equilibrium under three forces:

F_1 = 10 \text{ N}

east,

F_2 = 10 \text{ N}

north. What is the magnitude and direction of the third force

F_3

1
For equilibrium, $F_3$ must be equal and opposite to the resultant of $F_1$ and $F_2$ .
2
Resultant of $F_1$ and $F_2$ : $R = \sqrt{10^2 + 10^2} = 10\sqrt{2} \approx 14.1 \text{ N}$ at $45°$ north of east.
3
$F_3 = 14.1 \text{ N}$ directed $45°$ south of west.

Answer

F_3 \approx 14.1 \text{ N at } 45° \text{ south of west}

Equilibrium requires that the vector sum of all forces is zero. The third force must exactly cancel the resultant of the other two.

About Equilibrium

A state in which all forces acting on an object balance so that the net force equals zero and there is no acceleration.

A [formula] lamp hangs from a single vertical cord. What is the tension in the cord?

A [formula] sign hangs from two cables, each making a [formula] angle with the horizontal. What is t

A [formula] sign is held at rest by two vertical supports. One support pulls upward with [formula].