Gravity (\(g\)) can be calculated using the formula:
\[ g = \dfrac{W}{m} \]
Where:
- \(g\) is the acceleration due to gravity (in meters per second squared, \(\text{m/s}^2\))
- \(W\) is the weight (in newtons, N)
- \(m\) is the mass (in kilograms, kg)
Example 1: Calculating Gravity on Another Planet
Problem: An astronaut has a weight of 700 N on another planet. If their mass is 70 kg, what is the acceleration due to gravity on that planet?
Calculation:
Given:
- \(W = 700 \, \text{N}\)
- \(m = 70 \, \text{kg}\)
Using the formula:
\[ g = \dfrac{W}{m} \]
\[ g = \dfrac{700}{70} \]
\[ g = 10 \, \text{m/s}^2 \]
Answer: The acceleration due to gravity on that planet is 10 \(\text{m/s}^2\).
Example 2: Calculating Gravity on the Moon
Problem: A piece of equipment has a weight of 15.6 N on the Moon. If its mass is 2 kg, what is the acceleration due to gravity on the Moon?
Calculation:
Given:
- \(W = 15.6 \, \text{N}\)
- \(m = 2 \, \text{kg}\)
Using the formula:
\[ g = \dfrac{W}{m} \]
\[ g = \dfrac{15.6}{2} \]
\[ g = 7.8 \, \text{m/s}^2 \]
Answer: The acceleration due to gravity on the Moon is 7.8 \(\text{m/s}^2\).
Example 3: Calculating Gravity on Mars
Problem: A rover has a weight of 3536 N on Mars. If its mass is 400 kg, what is the acceleration due to gravity on Mars?
Calculation:
Given:
- \(W = 3536 \, \text{N}\)
- \(m = 400 \, \text{kg}\)
Using the formula:
\[ g = \dfrac{W}{m} \]
\[ g = \dfrac{3536}{400} \]
\[ g = 8.84 \, \text{m/s}^2 \]
Answer: The acceleration due to gravity on Mars is 8.84 \(\text{m/s}^2\).
