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All lessons Mechanics20 min

Forces and Free-Body Diagrams

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01
Hook
02
Explore
03
Formalize
04
Practice
05
Challenge
Interactive simulation
01

Hook

A 10 kg box sits dead still on the floor. Gravity is pulling it down with about 98 N the whole time — a force big enough to lift a small child. So why doesn't the box crash through to the floor below?

02

Explore

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03

Formalize

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04

Practice

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05

Challenge

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Spoilers

Forces and Free-Body Diagrams — summary and key formula

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The question

A 10 kg box sits dead still on the floor. Gravity is pulling it down with about 98 N the whole time — a force big enough to lift a small child. So why doesn't the box crash through to the floor below?

Something must be pushing back up with exactly 98 N. To predict how anything moves, you first have to find every force acting on it — and that is what a free-body diagram is for.

The key idea

A force is a push or pull, measured in newtons (N) and having a direction. The common ones: weight W = mg (gravity, always down), the normal force N (a surface pushing perpendicular to itself), an applied push or pull, friction f (opposes sliding, up to a limit), and tension T (a rope or string pulling along its length). A free-body diagram strips away everything else: draw the object as a dot or box, then draw each force as an arrow starting at the object and pointing the way the force acts. The NET force is the vector sum of those arrows — add them tip-to-tail. Balanced forces (net = 0) mean no acceleration; unbalanced forces (net ≠ 0) accelerate the object in the net direction.

The whole skill is: (1) name every force touching or acting on the object, (2) draw each as an arrow from the object, (3) add them. Forces along the same line just add or subtract — up versus down, right versus left. In the simulation the floor's normal force always grew to cancel weight, and friction grew to cancel the push until it hit its μN limit; both are examples of forces balancing to a net of 0. Only when one direction wins — like a 50 N push beating 39 N of friction — is there a net force, and then a = F_net/m tells you the acceleration. This is the foundation for Newton's laws in the next lesson. **All forms:** ΣF=ma⇒a=ΣF/m\Sigma F = ma \Rightarrow a = \Sigma F/mΣF=ma⇒a=ΣF/m, and when a=0a = 0a=0 every force must be cancelled by another. **Limiting case:** equilibrium (a=0a = 0a=0) makes the diagram close into balanced pairs; in free fall everything vanishes except mgmgmg — and N=0N = 0N=0 is exactly what a scale reads in a falling lift. **Connect it:** an FBD is Newton's second law drawn as arrows: the vector sum of what you sketch IS mamama. If your arrows don't add up to the motion you observe, a force is missing or invented.

The formula

F⃗net=∑F⃗,a=Fnetm\vec{F}_{net} = \sum \vec{F}, \qquad a = \frac{F_{net}}{m}Fnet​=∑F,a=mFnet​​
  • ·F_net = the single arrow you get by adding every force vector; ΣF means 'sum of all forces' (right minus left
  • ·up minus down); m = mass in kg; a = acceleration in m/s²
  • ·pointing the same way as F_net. If F_net = 0 the object keeps its current velocity.

Common mistake

Drawing forces that aren't real — like a 'force of motion' pushing it along. Only draw genuine pushes and pulls from other objects, then add them as vectors.

What to remember

  • ·A free-body diagram shows every real force ON one object as an arrow.
  • ·Net force = the vector sum of those arrows.
  • ·Balanced forces (net = 0) give constant velocity, not necessarily rest.