Newton’s Laws, Part 2

So I left off last time with the equation form of Newton’s second law: F = ma. It is important to use consistent units for the three quantities, the force F, the mass m, and the acceleration a.

Now in the USA, they use English units where the unit for acceleration is ft/sec² (feet per second squared), the unit of mass is something called a slug, and the unit for force is lbf (pound-force). We will not be using these units.

In the civilised world (I’m not biased), we use SI units. SI comes from the French Système international  which means the international system of units. For our equation, these units are kg (kilogram) for mass, m/sec² (meters/second squared) for acceleration, and the combination of these units on the right side of F = ma gives kg×m/sec² as the unit of force. This unit is given a special name in SI units, the newton, N, in honour of guess who. So 1 N is the force required to accelerate 1 kg of mass, 1 m/sec². 1 N is about the force an average size apple exerts on your hand.

Now I said I would also explain the difference between mass and weight. Weight is a force exerted by an object due to gravity. An objects weight changes when measured on different planets or moons. Its mass however, is an intrinsic property and remains unchanged regardless of where the object is. Mass is the amount of stuff that makes up the object.

Now the confusion between these two things arises because we commonly use weight, say in kilograms, to mean force. We feel the weight of a 1 kg object in our hands. But this unit is really a kilogram-force (kgf). A kilogram in SI units is a unit of mass, not weight. But fortunately, an object on earth that exerts a force of 1 kgf due to gravity, is defined as having a mass of 1 kg, so it is easy to interchange these units on earth. But elsewhere, the object will exert a different force (kgf) due to gravity but it will still be an object of 1 kg mass.

The kilogram-force unit is not an SI unit – we just naturally use it in everyday conversation. As seen before, the newton (N) is the SI unit of force. So what is the weight of a 1 kg mass in SI units? On earth, when you drop something from a height, its velocity starts as 0 m/s but its speed increases as time goes on. This is why you can jump from a half a meter height without injuring yourself but will do considerable damage if you jump from a 50 meter height. Increasing speed means acceleration. So there is an acceleration due to gravity on earth as well as other planets. On earth, the acceleration due to gravity is 9.8 m/sec². When an object is dropped on earth, its speed increases by 9.8 m/sec every second.

So if we want to calculate the weight of a 1 kg object, we use Newtons second law F = ma where we use the acceleration due to gravity for a:

F = 1 kg × 9.8 m/sec² = 9.8 N

If you want to know your weight in newtons, just take your mass in kg (which equals your weight in kgf), and multiply by 9.8. Your weight in newtons is almost 10 times your weight in kgf, which explains why people prefer to use kgf.