PhysicsIntroductory PhysicsHigh school

Forces and Newton's Laws

Free-body diagrams and net force.

A force is a push or pull, measured in newtons. Newton's first law says an object keeps its velocity unless a net force acts on it. The second law, $F_{\text{net}} = ma$ , says the net force sets the acceleration. The third law says forces come in equal and opposite pairs acting on different objects.

Solving force problems starts with a free-body diagram: draw the object alone and every force on it, such as weight $mg$ , normal force, tension, friction and applied forces. Then add the forces along each axis and apply Newton's second law separately in each direction.

Key terms

Newton's second law: Net force equals mass times acceleration.
$\sum F = ma$

Key ideas

Weight $W = mg$ , with $g \approx 9.8$ m/s².
Kinetic friction $f = \mu_k N$ ; static friction can be anything up to $\mu_s N$ .
On an incline, split weight into $mg\sin\theta$ along the slope and $mg\cos\theta$ into it.
Equilibrium means zero net force, not zero forces.

Worked example

A 10 kg box is pulled across a floor with 50 N. The coefficient of kinetic friction is 0.3. Find its acceleration.

Normal force: $N = mg = 98$ N.
Friction: $f = 0.3 \times 98 = 29.4$ N.
Net force: $50 - 29.4 = 20.6$ N.
$a = \frac{20.6}{10} = 2.06$ m/s².

Answer: $2.06$ m/s²

Common mistakes

Treating the third-law pair as cancelling on the same object.
Using mass in kilograms as if it were weight in newtons.
Assuming the normal force always equals $mg$ , even on inclines or with vertical pulls.

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.What net force gives a 1200 kg car an acceleration of 2.5 m/s²?
Show answer
$3000$ N
2.What is the weight of a 65 kg person (use $g = 9.8$ )?
Show answer
$637$ N
3.A 4 kg object feels a net force of 18 N. Find its acceleration.
Show answer
$4.5$ m/s²

Key terms

Key ideas

Worked example

Common mistakes

Practice questions

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