Understanding how to determine the force (\(F\)) acting on an object is essential in physics. The force can be calculated using the formula:
\[ F = m \cdot a \]
Where:
- \(F\) is the force acting on the object (in newtons, N)
- \(m\) is the mass of the object (in kilograms, kg)
- \(a\) is the acceleration of the object (in meters per second squared, m/s²)
Example 1: Calculating the Force on a Car
Problem: A car with a mass of 1200 kg accelerates at a rate of 3 m/s². What is the force acting on the car?
Calculation:
Given:
- \(m = 1200 \, \text{kg}\)
- \(a = 3 \, \text{m/s}^2\)
Using the formula:
\[ F = m \cdot a = 1200 \cdot 3 = 3600 \, \text{N} \]
Answer: The force acting on the car is 3600 N.
Example 2: Calculating the Force on a Bicycle
Problem: A bicycle with a mass of 15 kg accelerates at a rate of 2 m/s². What is the force acting on the bicycle?
Calculation:
Given:
- \(m = 15 \, \text{kg}\)
- \(a = 2 \, \text{m/s}^2\)
Using the formula:
\[ F = m \cdot a = 15 \cdot 2 = 30 \, \text{N} \]
Answer: The force acting on the bicycle is 30 N.
Example 3: Calculating the Force on a Rocket
Problem: A rocket with a mass of 500 kg accelerates at a rate of 20 m/s². What is the force acting on the rocket?
Calculation:
Given:
- \(m = 500 \, \text{kg}\)
- \(a = 20 \, \text{m/s}^2\)
Using the formula:
\[ F = m \cdot a = 500 \cdot 20 = 10000 \, \text{N} \]
Answer: The force acting on the rocket is 10000 N.
