Weight (\(W\)) is the force exerted by gravity on an object. It can be calculated using the formula:
\[ W = m \cdot g \]
Where:
- \(W\) is the weight (in newtons, N)
- \(m\) is the mass (in kilograms, kg)
- \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\) on Earth)
Difference Between Weight and Mass
- Mass: Mass is a measure of the amount of matter in an object and is measured in kilograms (kg). It is a scalar quantity and does not change regardless of location.
- Weight: Weight is the force exerted by gravity on an object's mass and is measured in newtons (N). It is a vector quantity and depends on the local gravitational field strength.
Example 1: Calculating the Weight of a Person
Problem: A person has a mass of 70 kg. What is their weight on Earth?
Calculation:
Given:
- \(m = 70 \, \text{kg}\)
- \(g = 9.8 \, \text{m/s}^2\)
Using the formula:
\[ W = m \cdot g \]
\[ W = 70 \cdot 9.8 \]
\[ W = 686 \, \text{N} \]
Answer: The weight of the person is 686 N.
Example 2: Calculating the Weight of a Book
Problem: A book has a mass of 1.5 kg. What is its weight on Earth?
Calculation:
Given:
- \(m = 1.5 \, \text{kg}\)
- \(g = 9.8 \, \text{m/s}^2\)
Using the formula:
\[ W = m \cdot g \]
\[ W = 1.5 \cdot 9.8 \]
\[ W = 14.7 \, \text{N} \]
Answer: The weight of the book is 14.7 N.
Example 3: Calculating the Weight of a Car
Problem: A car has a mass of 1200 kg. What is its weight on Earth?
Calculation:
Given:
- \(m = 1200 \, \text{kg}\)
- \(g = 9.8 \, \text{m/s}^2\)
Using the formula:
\[ W = m \cdot g \]
\[ W = 1200 \cdot 9.8 \]
\[ W = 11760 \, \text{N} \]
Answer: The weight of the car is 11760 N.
