Calculating Acceleration from Force and Mass

Understanding the relationship between force, mass, and acceleration is fundamental in physics. This relationship is described by Newton's Second Law of Motion. The question asks us to calculate the acceleration produced when a specific force is applied to a body of a given mass.

Understanding Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It also states that the direction of the acceleration is the same as the direction of the net force. The mathematical formula for this law is:

\( F = m \times a \)

Where:

• \( F \) is the net force applied (measured in Newtons, N)
• \( m \) is the mass of the object (measured in kilograms, kg)
• \( a \) is the acceleration produced (measured in meters per second squared, m/s\(^2\))

In this problem, we are given the force and the mass, and we need to find the acceleration. We can rearrange the formula to solve for acceleration:

\( a = \frac{F}{m} \)

Applying the Formula to Find Acceleration

Let's identify the given values from the problem:

• Force (\( F \)) = 20 N
• Mass (\( m \)) = 10 kg

Now, we substitute these values into the rearranged formula for acceleration:

\( a = \frac{20 \text{ N}}{10 \text{ kg}} \)

Performing the division:

\( a = 2 \text{ m/s}^2 \)

Result and Units

The calculation shows that the acceleration produced is 2 m/s\(^2\). The units work out correctly because 1 Newton is defined as 1 kg \(\times\) m/s\(^2\). So, \(\frac{\text{N}}{\text{kg}} = \frac{\text{kg} \times \text{m/s}^2}{\text{kg}} = \text{m/s}^2\).

Therefore, if a force of 20 N is applied on a body with a mass of 10 kg, the acceleration produced will be 2 m/sec\(^2\).

Revision Table: Force, Mass, and Acceleration

Additional Information: Details on Newton's Second Law

Newton's Second Law is crucial for understanding how forces cause motion. It's not just about the magnitude of the force, but also the mass of the object. A larger force causes greater acceleration for the same mass, while a larger mass results in less acceleration for the same force. The law is vectoral, meaning the direction of acceleration is always in the direction of the net force.

In many introductory problems, we consider only a single force acting on an object or multiple forces that can be combined into a single net force. For more complex situations, we might need to consider forces in different directions and use vector addition to find the net force before calculating the acceleration.

This law is a cornerstone of classical mechanics and is used extensively in physics and engineering to predict the motion of objects under the influence of forces.