Newton's Second Law of Motion

Definition of Newton's Second Law

Newton's Second Law of Motion states: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The acceleration is in the same direction as the net force.

Explanation

Newton's Second Law explains how forces cause acceleration. Acceleration refers to the rate of change of an object's velocity.

• Force: A force is a push or a pull. The greater the force, the greater the acceleration, assuming mass remains constant.
• Mass: Mass is the measure of an object's resistance to acceleration. The greater the mass, the smaller the acceleration for the same amount of force.
• Acceleration: Acceleration is the change in velocity of the object. It’s related to both the magnitude of the net force and the mass of the object.

Formula

Newton's Second Law is quantitatively expressed with the formula:

F = ma

Where:

• F is the net force acting on the object (measured in Newtons, N).
• m is the mass of the object (measured in kilograms, kg).
• a is the acceleration of the object (measured in meters per second squared, m/s²).

This formula shows that acceleration depends directly on the net force and inversely on the mass.

Real-World Applications

• Pushing a Shopping Cart: The harder you push (greater force), the faster the cart accelerates. A heavier cart (more mass) is harder to accelerate with the same force.
• A Rocket Launch: Rockets need a large force to overcome gravity and their own mass in order to achieve liftoff and accelerate upward.
• Throwing a Baseball: A player can achieve a greater acceleration (faster pitch) of the baseball by exerting a larger force on it.
• Car Acceleration: A car accelerates faster when a greater force is applied to it (by the engine), and it’s harder to accelerate if it has a larger mass.

Reference to Middle School Physical Science

In middle school physical science, Newton's Second Law is typically covered with:

• An emphasis on how forces cause changes in velocity (acceleration).
• An investigation of the relationship between force and acceleration.
• An investigation of the relationship between mass and acceleration.
• The introduction of the F=ma formula.
• Use of examples from everyday life to explain the concept.

Connections to NGSS Science Standards

Here's how Newton's Second Law aligns with key science education framework components:

• Disciplinary Core Idea (DCI):
  • PS2.A Forces and Motion: The change in an object's motion is proportional to the net force on it, and the inertia of the object.
• Crosscutting Concept (CCC):
  • Cause and Effect: Newton’s Second Law directly illustrates the cause and effect relationship between forces and motion.
• Science and Engineering Practice (SEP):
  • Developing and Using Models: Students can use simulations or diagrams to represent and predict how forces, mass, and acceleration relate. This simulation directly applies this concept.
  • Using Mathematics and Computational Thinking: Students use F=ma to calculate force, mass, or acceleration, and use the results to make predictions.
• Performance Expectation (PE):
  • MS-PS2-2: Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.