Newton's second law calculations | Physics | Khan Academy

Introduction

This tutorial will guide you through the calculations based on Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. By the end of this guide, you'll understand how to calculate acceleration, net force, and applied force in various scenarios.

Step 1: Understanding Newton's Second Law

Newton's second law is expressed by the formula:

[ F = m \cdot a ]

Where:

• ( F ) is the net force (in Newtons)
• ( m ) is the mass of the object (in kilograms)
• ( a ) is the acceleration (in meters per second squared)

Key Points

• The net force is the total force acting on an object after all opposing forces are considered.
• If you know the mass and acceleration, you can rearrange the formula to find the net force:

[ a = \frac{F}{m} ]

Or if you know the net force and mass, you can find the acceleration:

[ a = \frac{F}{m} ]

Step 2: Example Calculation - Acceleration of an Elevator

Consider an elevator with a mass of 500 kg that is subject to a net force of 2000 N.

Calculation Steps

1. Identify the mass of the elevator: ( m = 500 ) kg.
2. Identify the net force acting on the elevator: ( F = 2000 ) N.
3. Use the formula to calculate acceleration:

[ a = \frac{F}{m} = \frac{2000 , \text{N}}{500 , \text{kg}} = 4 , \text{m/s}^2 ]

Practical Advice

• Ensure to consider all forces acting on the object (gravity, tension, friction, etc.) when calculating the net force.
• Remember that if the object is moving upward against gravity, you must account for gravitational force.

Step 3: Example Calculation - Applied Force on a Sled

Consider a sled with a mass of 100 kg that experiences an acceleration of 2 m/s². To find the applied force needed to achieve this acceleration, follow these steps:

Calculation Steps

1. Identify the mass of the sled: ( m = 100 ) kg.
2. Identify the desired acceleration: ( a = 2 , \text{m/s}^2 ).
3. Use the formula to calculate the net force:

[ F = m \cdot a = 100 , \text{kg} \cdot 2 , \text{m/s}^2 = 200 , \text{N} ]

Practical Advice

• This force is what you need to apply to the sled to achieve the specified acceleration.
• In real-world scenarios, also consider frictional forces that may oppose the applied force.

Conclusion

In this tutorial, you learned how to apply Newton's second law to calculate acceleration and the necessary net force for given mass scenarios. Understanding these calculations is essential in physics and can be applied to various real-world situations, such as vehicle dynamics, elevator systems, and sports mechanics. For further practice, consider exploring different masses and forces to deepen your understanding of motion and forces.