Forces and Newton's Laws of Motion

The Mechanical Comprehension Test (MCT) is the most time-pressured section of the OAR with 30 questions in just 15 minutes — roughly 30 seconds per question. You need to recognize physics concepts immediately and apply them without hesitation. There is no time for working through problems from scratch.

The MCT at a Glance

Newton's Three Laws of Motion

First Law: Inertia

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force.

What it means practically:

• A book on a table stays put until you push it
• A hockey puck on ice keeps sliding until friction or a wall stops it
• A satellite in space keeps moving because there is essentially no friction
• Passengers lurch forward when a car brakes suddenly — their bodies want to keep moving

Inertia depends on mass. A heavier object has more inertia and is harder to start or stop.

Second Law: F = ma

The net force on an object equals its mass multiplied by its acceleration.

F = ma is the most important equation for the MCT.

Key implications:

• More force → more acceleration (for the same mass)
• More mass → less acceleration (for the same force)
• If acceleration = 0, the net force = 0 (object is in equilibrium)

Example: What force is needed to accelerate a 50 kg object at 3 m/s²? F = 50 × 3 = 150 N

Example: A 1,000 kg car experiences a net force of 4,000 N. What is its acceleration? a = F/m = 4,000/1,000 = 4 m/s²

Third Law: Action-Reaction

For every action, there is an equal and opposite reaction.

Key points:

• The forces act on DIFFERENT objects
• They are equal in magnitude and opposite in direction
• They exist simultaneously

Examples:

• When you push against a wall, the wall pushes back with equal force
• A rocket expels gas downward, and the reaction force pushes the rocket upward
• When you walk, your foot pushes backward on the ground, and the ground pushes your foot forward

Common misconception: If action and reaction are equal, why does anything accelerate? Because the forces act on different objects. When you push a box, you exert force on the box (it accelerates) and the box exerts force on you (but you have the ground holding you in place).

Types of Forces

Weight vs. Mass

On Earth: g ≈ 9.8 m/s² (often rounded to 10 m/s² for quick calculations)

Example: A crate has a mass of 25 kg. What is its weight on Earth? W = 25 × 9.8 = 245 N (or approximately 25 × 10 = 250 N)

Friction

Static vs. Kinetic Friction

Key insight: Static friction is greater than kinetic friction. That is why it takes more force to START pushing a heavy box than to KEEP it moving.

• μ (mu) = coefficient of friction (depends on surface materials)
• N = normal force (usually equal to weight on a flat surface)

Example: A 40 kg crate sits on a floor with μ_k = 0.3. What force is needed to keep it sliding at constant speed?

• Weight = 40 × 10 = 400 N
• Normal force = 400 N (flat surface)
• Friction = 0.3 × 400 = 120 N

Since constant speed means zero acceleration, the applied force must exactly equal friction: 120 N.

Free-Body Diagrams

A free-body diagram shows all forces acting on a single object. For the MCT, you do not need to draw them, but you need to think through them quickly.

Equilibrium (No Acceleration)

When an object is not accelerating, all forces balance:

• ΣF = 0 (sum of all forces = zero)
• Forces up = Forces down
• Forces left = Forces right

Net Force (Acceleration)

When forces do not balance, the object accelerates in the direction of the net force.

Example: A 10 kg object has 50 N pushing right and 30 N pushing left.

• Net force = 50 - 30 = 20 N to the right
• Acceleration = 20/10 = 2 m/s² to the right