Mass (\(m\)) can be calculated using the formula:
\[ m = \dfrac{W}{g} \]
Where:
- \(m\) is the mass (in kilograms, kg)
- \(W\) is the weight (in newtons, N)
- \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\) on Earth)
Example 1: Calculating the Mass of a Person
Problem: A person has a weight of 686 N on Earth. What is their mass?
Calculation:
Given:
- \(W = 686 \, \text{N}\)
- \(g = 9.8 \, \text{m/s}^2\)
Using the formula:
\[ m = \dfrac{W}{g} \]
\[ m = \dfrac{686}{9.8} \]
\[ m = 70 \, \text{kg} \]
Answer: The mass of the person is 70 kg.
Example 2: Calculating the Mass of a Book
Problem: A book has a weight of 14.7 N on Earth. What is its mass?
Calculation:
Given:
- \(W = 14.7 \, \text{N}\)
- \(g = 9.8 \, \text{m/s}^2\)
Using the formula:
\[ m = \dfrac{W}{g} \]
\[ m = \dfrac{14.7}{9.8} \]
\[ m = 1.5 \, \text{kg} \]
Answer: The mass of the book is 1.5 kg.
Example 3: Calculating the Mass of a Car
Problem: A car has a weight of 11760 N on Earth. What is its mass?
Calculation:
Given:
- \(W = 11760 \, \text{N}\)
- \(g = 9.8 \, \text{m/s}^2\)
Using the formula:
\[ m = \dfrac{W}{g} \]
\[ m = \dfrac{11760}{9.8} \]
\[ m = 1200 \, \text{kg} \]
Answer: The mass of the car is 1200 kg.
