Determining the mass (\(m\)) of an object using the force and acceleration is a fundamental concept in physics. The mass can be calculated using the rearranged formula:
\[ m = \dfrac{F}{a} \]
Where:
- \(m\) is the mass of the object (in kilograms, kg)
- \(F\) is the force acting on the object (in newtons, N)
- \(a\) is the acceleration of the object (in meters per second squared, m/s²)
Example 1: Calculating the Mass of a Truck
Problem: A force of 9000 N is applied to a truck, causing it to accelerate at a rate of 3 m/s². What is the mass of the truck?
Calculation:
Given:
- \(F = 9000 \, \text{N}\)
- \(a = 3 \, \text{m/s}^2\)
Using the formula:
\[ m = \dfrac{F}{a} = \dfrac{9000}{3} = 3000 \, \text{kg} \]
Answer: The mass of the truck is 3000 kg.
Example 2: Calculating the Mass of a Boat
Problem: A force of 200 N is applied to a boat, causing it to accelerate at a rate of 0.5 m/s². What is the mass of the boat?
Calculation:
Given:
- \(F = 200 \, \text{N}\)
- \(a = 0.5 \, \text{m/s}^2\)
Using the formula:
\[ m = \dfrac{F}{a} = \dfrac{200}{0.5} = 400 \, \text{kg} \]
Answer: The mass of the boat is 400 kg.
Example 3: Calculating the Mass of a Sled
Problem: A force of 50 N is applied to a sled, causing it to accelerate at a rate of 2.5 m/s². What is the mass of the sled?
Calculation:
Given:
- \(F = 50 \, \text{N}\)
- \(a = 2.5 \, \text{m/s}^2\)
Using the formula:
\[ m = \dfrac{F}{a} = \dfrac{50}{2.5} = 20 \, \text{kg} \]
Answer: The mass of the sled is 20 kg.
