Draw free-body diagrams showing all forces acting on an object, and use them to identify equilibrium (zero net force) and to find the net force in one direction (MA STE Introductory Physics, Motion and Forces).

What this topic is asking

A free-body diagram is the single most useful tool in mechanics, and the Massachusetts Introductory Physics MCAS expects you to draw and read one. You must show all the forces acting on an object as labeled arrows, then use the diagram to decide whether the object is in equilibrium (zero net force) and to find the net force in a given direction. This is the practice of developing and using a model applied to forces.

Drawing a free-body diagram

The rules for a good diagram are simple but strict:

1. Choose one object and draw only the forces acting on it. Do not include forces it exerts on other things (those belong on the other object's diagram).
2. Draw each force as an arrow from the object, pointing the way the force acts, with a longer arrow for a larger force.
3. Label every arrow: weight ($F_g$), normal force ($F_N$), tension ($T$), applied force ($F$), friction ($F_f$).

The usual forces and their directions:

• Weight ($F_g = mg$): always straight down.
• Normal force ($F_N$): perpendicular to the surface the object rests on.
• Tension ($T$): along a rope or string, pulling away from the object.
• Applied force: in the direction of the push or pull.
• Friction ($F_f$): along the surface, opposite to the motion.

Equilibrium

Equilibrium is not the same as "at rest." A skydiver falling at constant (terminal) velocity is in equilibrium, because the upward air resistance balances the downward weight, giving zero net force, even though the skydiver is moving fast. The test of equilibrium is always the net force, which you read straight off the balanced diagram.

Finding the net force from a diagram

Once the diagram is drawn, finding the net force is bookkeeping in each direction:

• Vertical: add the up forces and subtract the down forces (or vice versa). If the object does not accelerate vertically, these balance to zero, which often gives the normal force or a tension.
• Horizontal: add the right forces and subtract the left forces. The result is the horizontal net force, which goes into $F = ma$ to find the acceleration.

Try this

Q1. A box rests on a level table. Name the two forces on its free-body diagram and their directions. [2]

• Cue. Weight ($F_g$) downward and the normal force ($F_N$) upward.

Q2. A parachutist descends at constant velocity. Is the parachutist in equilibrium? Explain. [2]

• Cue. Yes; constant velocity means zero acceleration, so the net force is zero (the upward air resistance balances the downward weight), which is equilibrium.