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Physics 1/Newton's laws

Forces and Newton's laws

Why things accelerate: Newton's three laws, free-body diagrams, weight vs. mass, and friction. Anchored to OpenStax University Physics Vol. 1, Ch. 5 (§5.1–5.7) and Ch. 6 (§6.2).

Before you start — give these a try

Attempting first primes your brain for the lesson — even if you miss. Nothing is graded or saved; it's just a warm-up.

A 2.0 kg2.0\ \text{kg} box is pushed with 10 N10\ \text{N} while friction pushes back with 4.0 N4.0\ \text{N}. What is its acceleration (m/s²)?

A 5.0 kg5.0\ \text{kg} lamp hangs at rest from a single cord. What is the tension in the cord (N, use g=9.8g = 9.8)?

What you’ll be able to do

  • State Newton's three laws and identify action–reaction pairs.
  • Apply ∑F=ma\sum F = ma with a free-body diagram.
  • Separate weight (mgmg) from mass, and compute friction as f=μNf = \mu N.
1

The three laws

1st (inertia): with zero net force, velocity is constant (at rest or straight-line, steady speed). 2nd: ∑F⃗=ma⃗\sum \vec F = m\vec a — net force sets acceleration. 3rd: forces come in equal-and-opposite pairs on different bodies: if A pushes B, B pushes A back just as hard. (OpenStax §5.2–5.6.)

2

Mass vs. weight; free-body diagrams

Mass mm (kg) is how much inertia a body has; weight W=mgW = mg (newtons) is the gravitational force on it. To solve a problem, draw a free-body diagram: every force on the object as an arrow, then apply ∑F=ma\sum F = ma along each axis. (OpenStax §5.4, §5.7.)

3

Friction

Contact surfaces resist sliding. Kinetic friction is fk=μkNf_k = \mu_k N and static friction can be anything up to fsmax⁡=μsNf_s^{\max} = \mu_s N, where NN is the normal force. On a flat floor with no vertical acceleration, N=mgN = mg. (OpenStax §6.2.)

Newton's second law

∑F⃗=ma⃗\sum \vec F = m\vec a (apply component by component).

Intuition. Acceleration points along the net force and shrinks as mass grows — the same push moves a cart more than a truck.
Newton's third law

F⃗A→B=− F⃗B→A\vec F_{A\to B} = -\,\vec F_{B\to A}.

Intuition. The pair acts on two different objects, so the forces never cancel on the same body — that's why you can still accelerate.

Worked examples

Example 1

A 2.0 kg2.0\ \text{kg} box on a floor is pushed with a horizontal force of 10 N10\ \text{N}; kinetic friction opposes it with 4.0 N4.0\ \text{N}. Find the acceleration.

  1. 1

    Net horizontal force: ∑F=10−4.0=6.0 N\sum F = 10 - 4.0 = 6.0\ \text{N}.

  2. 2

    Second law: a=∑F/m=6.0/2.0=3.0 m/s2a = \sum F / m = 6.0/2.0 = 3.0\ \text{m/s}^2 in the push direction.

Answer. a=3.0 m/s2a = 3.0\ \text{m/s}^2.