Newton's Second Law Calculator: Force, Mass, Acceleration

What is Newton's Second Law?

Newton's Second Law of Motion is a fundamental principle in physics that describes the relationship between an object's mass, the force acting upon it, and its resulting acceleration. This law forms the foundation for classical mechanics and helps us understand how objects move when forces are applied to them.

Formula

Newton's Second Law is expressed by the following equation:

\[ F = ma \]

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)

Calculation Steps

Let's calculate the force required to accelerate a 1000 kg car from 0 to 27.8 m/s (100 km/h) in 10 seconds:

1. Identify the known values:
   • Mass (m) = 1000 kg
   • Initial velocity (v₀) = 0 m/s
   • Final velocity (v) = 27.8 m/s
   • Time (t) = 10 s
2. Calculate the acceleration: \[ a = \frac{v - v₀}{t} = \frac{27.8 - 0}{10} = 2.78 \text{ m/s²} \]
3. Apply Newton's Second Law: \[ F = ma \]
4. Substitute the known values: \[ F = 1000 \text{ kg} \cdot 2.78 \text{ m/s²} \]
5. Perform the calculation: \[ F = 2780 \text{ N} \]

Example and Visual Representation

Let's visualize Newton's Second Law with our example:

This visual representation illustrates:

• The mass of the car (1000 kg) represented by the blue rectangle
• The acceleration (2.78 m/s²) shown by the green arrow
• The resulting force (2780 N) depicted by the red arrow