The relationship between weight and mass
The Weight Formula: P = m x g
The Formula to Know
The weight P of an object is related to its mass m by the formula:
P = m x g
where P is the weight in newtons (N), m is the mass in kilograms (kg), and g is the strength of gravity, expressed in newtons per kilogram (N/kg).
The Value of g on Earth
On Earth, at the surface, g is about 9.8 N/kg. To simplify calculations in middle school, g = 10 N/kg is often used.
Calculation Example
A mass m = 5 kg. Its weight on Earth is:
P = m x g = 5 x 10 = 50 N
Finding the Mass from the Weight
The formula can also be reversed to calculate a mass if the weight and g are known: m = P / g. For example, if P = 300 N and g = 10 N/kg, then m = 300 / 10 = 30 kg.
| Mass (kg) | g (N/kg) | Weight (N) |
|---|---|---|
| 1 | 10 | 10 |
| 8 | 10 | 80 |
| 60 | 10 | 600 |
Common Pitfall
Don't mix up the units! In the formula P = m x g, the mass must be in kilograms, not grams. If a mass is given in grams, it must first be converted to kg (divide by 1000) before calculating the weight.