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Newton's Second Law

Newton's second law states that force is equal to the rate of change of momentum; for constant mass, it is commonly used as F = ma.

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Student-friendly explanation

The law connects force, mass, and acceleration. For the same mass, a greater force gives greater acceleration. For the same force, a greater mass gives smaller acceleration.

How to write this in exams

  1. 1

    Start with the exact idea

    Newton's second law states that force is equal to the rate of change of momentum; for constant mass, it is commonly used as F = ma.

  2. 2

    Then show how to use it

    List given values, choose F = ma, rearrange if needed, substitute correctly, calculate, and attach SI unit.

  3. 3

    Add one concrete example

    A 5 kg object given an acceleration of 4 m/s² needs a force of 20 N.

  4. 4

    Avoid this incomplete answer

    For F = 50 N and m = 10 kg, writing a = 500 m/s² is wrong because force must be divided by mass.

Definition

Newton's second law states that force is equal to the rate of change of momentum; for constant mass, it is commonly used as F = ma.

Example

A 5 kg object given an acceleration of 4 m/s² needs a force of 20 N.

Rule to remember

F = ma, where F is force in N, m is mass in kg, and a is acceleration in m/s².

Memory hook

Second law: force decides acceleration after mass is considered.

Examples and method

Worked example

If m = 10 kg and F = 50 N, then a = F/m = 50/10 = 5 m/s².

Method to apply

List given values, choose F = ma, rearrange if needed, substitute correctly, calculate, and attach SI unit.

Diagram support

A block with a force arrow and acceleration arrow can show that acceleration is in the direction of net force.

How CBSE asks it

Numericals ask for force, mass, or acceleration, and conceptual questions compare two objects under the same force.

Avoid common mistakes

Common confusion

Students may use F = m/a or forget to convert units before substitution.

Common wrong answer

For F = 50 N and m = 10 kg, writing a = 500 m/s² is wrong because force must be divided by mass.

Exam tip

Write the formula first, substitute with units, then give the answer in newton.

Quick check

What happens to acceleration if the same force acts on a larger mass?

The acceleration becomes smaller because acceleration is inversely related to mass when the applied force remains the same.

Study the newton's second law diagram carefully

Use the labelled diagram to keep newton's second law clear in short answers and revision.

What this diagram makes clear

This diagram keeps the labels and direction of newton's second law in the right order.

Where this helps in exams

Use this for labelled diagram work and short exam answers on newton's second law.

Revision cue

Revise newton's second law through the labels before writing the answer.

Answer writing and exam use

1-mark answer

Newton's second law states that force is equal to the rate of change of momentum; for constant mass, it is commonly used as F = ma.

2-mark answer

Newton's second law states that force is equal to the rate of change of momentum; for constant mass, it is commonly used as F = ma. F = ma, where F is force in N, m is mass in kg, and a is acceleration in m/s². A 5 kg object given an acceleration of 4 m/s² needs a force of 20 N.

3-mark answer

The law connects force, mass, and acceleration. For the same mass, a greater force gives greater acceleration. For the same force, a greater mass gives smaller acceleration. F = ma, where F is force in N, m is mass in kg, and a is acceleration in m/s². If m = 10 kg and F = 50 N, then a = F/m = 50/10 = 5 m/s². Numericals ask for force, mass, or acceleration, and conceptual questions compare two objects under the same force. For F = 50 N and m = 10 kg, writing a = 500 m/s² is wrong because force must be divided by mass.
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