Forces and Free-Body Diagrams
Identify contact and field forces, draw free-body diagrams, and use net force to reason about balanced and unbalanced situations.
A lesson of Physics, in Forces and Newton Laws, about 10 minutes.
By the end of this lesson, you will be able to identify all forces on an object, draw accurate free-body diagrams, and apply Newton's second law to solve force problems.
The Concept of Force
A force is an interaction between objects that causes (or tends to cause) acceleration or deformation. Forces are vectors — they have magnitude and direction.
Contact forces: require physical contact.
- Normal force ($\vec{N}$): perpendicular to surface; prevents objects from passing through each other
- Friction ($\vec{f}$): parallel to surface; opposes sliding motion
- Tension ($\vec{T}$): along a rope or cable; pulls toward the rope
Field forces (action at a distance):
- Gravity ($\vec{W} = m\vec{g}$): downward; magnitude $mg$
- Electromagnetic forces
- Nuclear forces
Free-Body Diagrams (FBDs)
A free-body diagram shows all forces acting on ONE object, drawn as vectors originating from the object's center.
Rules:
- Draw only the object (often as a dot or box)
- Draw ONLY forces acting ON this object (not forces it exerts on other objects)
- Show each force as an arrow with label and direction
- Do not include velocity, acceleration, or motion in the FBD itself
Newton's Second Law
$$\vec{F}_{\text{net}} = m\vec{a}$$
Sum of all forces = mass × acceleration
In component form: $$\sum F_x = ma_x \qquad \sum F_y = ma_y$$
If acceleration = 0: the object is in equilibrium (Newton's First Law). All forces balance.
Example 1 — Box on a Table
A 10 kg box rests on a horizontal table. Draw the FBD and find the normal force.
Forces on the box:
- Weight: $W = mg = 10 \times 9.8 = 98$ N downward
- Normal force: $N$ upward
Since box is at rest ($a = 0$):
$\sum F_y = 0 \implies N - W = 0 \implies N = 98$ N
Example 2 — Box Being Pushed
A 5 kg box on a frictionless floor is pushed with 30 N horizontally. Find acceleration.
FBD forces:
- Horizontal: $F = 30$ N (applied)
- Vertical: $W$ down, $N$ up (cancel)
$\sum F_x = ma_x \implies 30 = 5a \implies a = 6$ m/s²
Example 3 — Inclined Plane
A 4 kg block on a 30° frictionless incline. Find acceleration.