Physics · Grades 1–12

Forces & equilibrium · Quick reference

Reference sheet for Grades 1 to 12: balanced and unbalanced forces and action and reaction pairs. Watch the direction: a push moves something away from you; a pull moves it toward you.

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Rule and key idea

Push or pull?

Watch the direction: a push moves something away from you; a pull moves it toward you.

push: away from you · pull: toward you

Is this a push or a pull? Towing a wagon behind you by its handle. → a pull

Balanced and unbalanced forces

Add forces as vectors. Balanced forces (net force zero) leave velocity unchanged, so the object stays at rest or keeps moving steadily. An unbalanced force changes velocity.

net force = vector sum · net force ≠ 0 → acceleration in its direction

A crate on a frictionless surface has two horizontal forces on it: 35 N toward the east and 40 N toward the west. (Vertical forces balance.) What happens to the crate’s motion? → It accelerates toward the west.

Action and reaction pairs

Newton’s third law: forces come in pairs that are equal in size, opposite in direction, and act on two different objects. That is why they never cancel each other.

force of A on B = − force of B on A

A book rests on a table. Earth pulls the book down with its weight. What is the third-law partner of this force? → The book pulls Earth upward with an equal force.

Check yourself

Four practice questions on this topic. Try each one before you open the answer.

Two perpendicular forces of 120 N and 225 N act on a point. Find the magnitude of their resultant. Round to 3 decimal places if needed. Answer in N.
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255 N R = √(F₁² + F₂²) √(120² + 225²) = 255
A sliding block has normal force 101 N and kinetic friction coefficient 0.2. Find the friction-force magnitude in this model. Round to 3 decimal places if needed. Answer in N.
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20.2 N Fₖ = μₖN 0.2 × 101 = 20.2
A 3 kg cart has horizontal forces 11 N right and 53 N left. No other horizontal forces act. Taking right as positive, find its acceleration. Round to 3 decimal places if needed. Answer in m/s².
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-14 m/s² a = (Fright − Fleft)/m (11 − 53) / 3 = -14
A mass of 60 kg is in a model gravitational field of 10 N/kg. Find its weight. Round to 3 decimal places if needed. Answer in N.
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600 N Fᵍ = mg 60 × 10 = 600