Question

What is the metric, that is SI, unit of force, and how is it defined in terms of mass and acceleration?

Hint:

Start from Newton's second law, force equals mass times acceleration, and combine the SI units of mass and acceleration.

Answer 1

Step 1: Force is defined through Newton's second law of motion, which states that the force acting on a body equals the rate of change of its momentum, and for a constant mass this simplifies to force equals mass times acceleration, written as \( F = ma \).

Step 2: To build a unit of force in the metric SI system, we use the SI units already fixed for mass and acceleration, namely kilogram for mass and metre per second squared for acceleration.

Step 3: The SI unit of force is called the newton, symbol N, named after Sir Isaac Newton. It is defined as the amount of force that produces an acceleration of 1 metre per second squared in a body of mass 1 kilogram. In symbols, \( 1 \ N = 1 \ kg \times 1 \ m/s^2 \).

Step 4: Written out in base SI units, \( 1 \ N = 1 \ kg \cdot m \cdot s^{-2} \). For comparison, in the older CGS system the unit of force is the dyne, where 1 newton equals \( 10^5 \) dyne.

So the metric or SI unit of force is the newton, defined as the force needed to give a 1 kilogram mass an acceleration of 1 metre per second squared.