8.3 Force, Motion, and Newton's Laws

8.3 Force, Motion, and Newton's Laws

Why This Matters for the PUPCET

Mechanics questions in the PUPCET Science area follow a comfortable pattern: either a one-step computation using v = d/t, a = Δv/t, or W = mg, or a scenario asking which of Newton's laws explains an everyday event. Both reward memorizing a small set of formulas and, more importantly, understanding what each one means.

Scalar vs Vector Quantities

A scalar has magnitude (size) only; a vector has magnitude and direction. This distinction decides which word is correct in an exam item:

A jogger who runs one full 400-meter lap around an oval covers a distance of 400 m but has a displacement of zero, because she ends where she started. Same motion, different quantity.

Speed, Velocity, and Acceleration

• Speed = distance ÷ time: v = d/t, in meters per second (m/s).
• Velocity is speed in a stated direction — 12 m/s east is a velocity.
• Acceleration = change in velocity ÷ time: a = Δv/t, in meters per second squared (m/s²). Acceleration happens whenever velocity changes in size or direction — speeding up, slowing down (deceleration), or turning.

Worked example 1 (speed). A jeepney travels 120 meters along a straight road in 10 seconds. v = d/t = 120 ÷ 10 = 12 m/s.

Worked example 2 (acceleration). A tricycle speeds up from 2 m/s to 14 m/s in 4 seconds. a = (14 − 2) ÷ 4 = 12 ÷ 4 = 3 m/s².

Worked example 3 (rearranging). How far does a cyclist moving at a steady 8 m/s go in 15 seconds? Rearrange to d = vt = 8 × 15 = 120 m.

Common trap: mixing units. If a problem gives distance in kilometers and time in hours, stay consistent — km and hours give km/h; meters and seconds give m/s. Do not combine meters with hours. (To convert, 1 m/s = 3.6 km/h.)

Newton's Three Laws of Motion

First Law — the Law of Inertia. An object at rest stays at rest, and an object in motion keeps moving at the same speed and direction, unless an unbalanced force acts on it. Inertia is the tendency to resist changes in motion, and more mass means more inertia. Philippine examples: passengers lurch forward when a jeepney brakes suddenly (their bodies keep moving); dust flies off a rug when you beat it with a walis; a mango stays on the table when you yank the tablecloth fast enough. Misconception alert: objects do not slow down because motion naturally runs out — a rolling ball stops because friction, an unbalanced force, acts on it.

Second Law — F = ma. The acceleration of an object equals the net force on it divided by its mass. Double the force, double the acceleration; double the mass, half the acceleration for the same force. This is why an empty kariton is easy to push up to speed but the same push barely moves a fully loaded one. Worked example: a 10-kg cart pushed with a net force of 20 N accelerates at a = F/m = 20 ÷ 10 = 2 m/s².

Third Law — Action and Reaction. For every action force there is an equal and opposite reaction force. When you walk, your foot pushes the ground backward and the ground pushes you forward — that reaction is what moves you. A balloon rocket shoots forward because air rushes out backward; a swimmer pushes the water back and the water pushes her ahead. Misconception alert: action and reaction act on different objects (foot on ground, ground on foot), so they never cancel each other out. Forces that cancel act on the same object.

Friction and Gravity

Friction is a force that opposes sliding between surfaces in contact. Static friction keeps a resting object from starting to slide; kinetic (sliding) friction acts once it moves; rolling friction is much smaller, which is why wheels were such a breakthrough. Friction is useful — it lets your rubber shoes grip the pavement and lets jeepney brakes work — but it also wears out soles and machine parts, so we reduce it with lubricants like oil.

Gravity pulls every mass toward every other mass; near Earth's surface it gives falling objects a constant acceleration g ≈ 9.8 m/s² (sometimes rounded to 10 for quick estimates). Ignore air resistance and a dropped 1-peso coin and a dropped book hit the floor together — mass does not change how fast things fall.

Mass vs weight — the classic exam distinction:

Worked example. A student with a mass of 50 kg weighs W = 50 × 9.8 = 490 N on Earth.

Free-body intuition. To analyze any situation, picture the object alone and draw arrows for every force on it: gravity pulling down, the surface pushing up (the normal force), applied pushes or pulls, and friction opposing motion. If the arrows balance, the object keeps doing what it was doing — that is the first law again. If they do not balance, it accelerates in the direction of the net force.

Exam Tips

• Lurching, resisting, continuing — think inertia, the first law.
• Numbers with push, mass, and acceleration — use F = ma.
• Two objects pushing on each other — the third law.
• Check units before computing, and remember weight is a force in newtons, not kilograms.