Newton's Second Law
Newton's second law F=ma: force equals mass times acceleration.
Calculate force, mass, or acceleration with worked examples in SI and imperial units.
The Formula
F = ma
Force equals mass multiplied by acceleration. This is one of the most fundamental equations in physics.
Variables
| Symbol | Meaning |
|---|---|
| F | Force (measured in newtons, N) |
| m | Mass of the object (measured in kilograms, kg) |
| a | Acceleration (measured in meters per second squared, m/s²) |
Example 1
A 12 kg box is pushed across a floor with an acceleration of 3 m/s². What force is applied?
Identify the values: m = 12 kg, a = 3 m/s²
Apply the formula: F = ma = 12 × 3
F = 36 N
Example 2
A 1,500 kg car accelerates from rest to 20 m/s in 10 seconds. What is the net force?
First find acceleration: a = (v - u) / t = (20 - 0) / 10 = 2 m/s²
Apply the formula: F = ma = 1,500 × 2
F = 3,000 N
When to Use It
Use Newton's second law whenever you need to relate force, mass, and acceleration.
- Calculating the force needed to accelerate an object
- Finding the acceleration produced by a known force
- Determining the mass of an object from force and acceleration measurements
- Solving problems involving friction, tension, or applied forces
Key Notes
- F = ma applies to the net force — if a 50 N push is opposed by 10 N of friction, the net force is 40 N and the box accelerates at 40/m, not 50/m; forgetting to account for opposing forces is the most common mechanics error
- Mass and weight are different: mass (kg) is constant regardless of location; weight = mg is a force (N) that depends on local gravitational acceleration — on the Moon (g = 1.62 m/s²), your mass is unchanged but your weight is about 1/6 of Earth's
- The more precise form is F = dp/dt (rate of change of momentum), which reduces to F = ma only when mass is constant — for variable-mass systems like rockets (which expel propellant), the full derivative form leads to the Tsiolkovsky rocket equation
- Newton's third law pairs with the second: every force has an equal and opposite reaction, but the accelerations differ because each object has its own mass — a ball hitting a wall exerts the same force on the wall as the wall exerts on the ball, but the wall barely moves