Unit 2.5: Newton’s Second Law

Introduction

Newton’s Second Law describes the relationship between force, mass, and acceleration. It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This fundamental law is written mathematically as:

F = ma

Key Concepts

Force (\(F\)): A push or pull that causes an object to accelerate.
Mass (\(m\)): A measure of an object's resistance to acceleration (in kg).
Acceleration (\(a\)): The rate of change of velocity (\(m/s^2\)).
Net Force: The vector sum of all forces acting on an object.
Proportionality: If force increases, acceleration increases. If mass increases, acceleration decreases.

Tip: The unit of force is the Newton (N), where \( 1N = 1kg \cdot m/s^2 \).

Free-Body Diagrams and Newton’s Second Law

Free-body diagrams are essential for applying Newton’s Second Law. Follow these steps:

Draw a diagram of the object.
Identify and label all forces acting on the object.
Break forces into components (if needed).
Apply F = ma in the x and y directions.

Exam Strategy: Always analyze forces carefully. If acceleration is zero, net force must also be zero.

Applications of Newton’s Second Law

Objects in Free Fall: The acceleration due to gravity is \( 9.8m/s^2 \).
Pushing an Object: A greater force results in a greater acceleration.
Braking in a Car: The force applied by brakes determines the deceleration.

Mathematical Routines

Newton’s Second Law can be used to solve for force, mass, or acceleration:

If force and mass are known, solve for acceleration: \( a = \frac{F}{m} \).
If acceleration and mass are known, solve for force: \( F = ma \).
If force and acceleration are known, solve for mass: \( m = \frac{F}{a} \).

Tip: Always check that force and mass are in consistent SI units before solving.

Practice Activities

Activity 1: Calculating Acceleration

A 10 kg box is pushed with a force of 50 N. What is its acceleration? (Ignore friction.)

Activity 2: Net Force Calculation

A car of mass 1000 kg experiences a force of 4000 N forward and 1000 N backward (friction). What is its acceleration?

Activity 3: Elevator Problem

A person with a mass of 70 kg is in an elevator accelerating upward at \(2 m/s^2\). What is the normal force exerted by the floor of the elevator?

Summary & Exam Preparation Tips

Newton’s Second Law is crucial for understanding motion. Key takeaways:

Acceleration depends on both force and mass (F = ma).
Free-body diagrams help visualize net force and acceleration.
Forces must be summed as vectors, considering direction.
Friction, gravity, and normal forces must be included in problem-solving.

Mastering force problems will improve success on AP Physics exams.