Newton's second law of motion with a worked example.

Introduction

In the first lesson, I explained newtons first law of motion which is popularly called Inertia. The law defines what happens to a body in a state of rest or constant motion. If you missed that an want to check it out, you can click here.. In this lesson, we want to understand the second law of motion which describes how forces affect an object in motion.

Below is a correction definition of Newtons second law according to the Encyclopedia Britannica:

It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it source

Explaining the second law

• Momentum varies directly as the ForceThis second law of motion is so crucial to understanding how objects behave when some force acts on the. The law shows when a force acts on an object, it changes the size of its momentum and this change happens in the direction of the force. Because the momentum of the object is directly proportional to the force acting on it, the larger the force, the the bigger the momentum.

Trying to break it down more, it means that the force that would be required to move an object for 10 kilometers would be larger than the force that will push if for 5 kilometers. The bigger the force, the larger the momentum of the object. The law also shows that each objects momentum happens in the direction in which the force acts. That is reasonable and easy to understand. If the force acting on an object is facing the southern direction, the object would move towards south. If it is facing north, the object would still move along those lines.

• Mass varies inversely as acceleration: The second law as tries to explain the relationship between the mass of an object and its acceleration. The mass of an object affects its momentum or acceleration with respect to the force acting on it. The law shows that the objects mass varies inversely as the acceleration produced by the force. In summary, the bigger the mass of the object, the smaller its momentum and vice versa.

Understanding the relationship between mass and acceleration in simple terms, a if a constant forces acts on a weight of 10 kg, it make it accelerate over a specific distance. But if the same force is acts on a weight of 20kg, the distance it would move would be smaller than the 10kg weight. Because the weight is not heavier, the distance moved is smaller. So acceleration of objects varies inversely as their mass, but directly to the force and in the direction of the force.

Representing the quantities mathematically

At this point in the discussion, it is understood that newtons second law of motion tries to describe the quantitative relationship between force, mass and acceleration. The explalantion above has help to show that the bigger the force, the larger the acceleration or moment. The bigger the mass, the smaller the accelertion.

Trying to represent the three quantities mathematically is essential as it helps scientists to determine the effect of each quantity on an object acted upon by an external force. So the mathematical relationship is thus:

From the equation above,
F = force acting on the object (SI unit of force is Newton)
m = mass of the object (SI unit of force is Kilograms)
a = acceleration (SI unit is meters per second squared)

Confirming the law with a worked example

A block of mass 800g is pushed on the surface of a desk by a force of 30N. The force of friction which opposes the motion is 10N. How far was the weight moved?

Solution

Remember that f=ma

F = 30 - 10 = 20N
m = 800g (converting to SI unit of kg, we have) 800/1000 = 0.8kg
a = ?

Since f=ma, we have,

20 = 0.8 x a (making a the subject, we have)

a = 20/0.8
a = 25m/s²

Lets try to increase the mass of the block and see if the acceleration reduces. Assuming we doubled the mass to 1600g.

m= 1600g, converting to kg, we have 1600/1000 = 1.6kg

20 = 1.6 x a. Making a the subject, we have
a = 20/1.6
a = 12.5m/s²

Observation: Notice that when the mass was 800g, the acceleration was
25m/s². But when the mass was doubled to 1600g, the acceleration was halved to 12.5m/s². That confirms the accuracy of Newtons second law of motion which states that acceleration of an object acted upon by some external force is inversely proportional to its mass.

Conclusion

Newtons second law accurately helps us understand the relationship between three important quantities and this has formed a foundation for advanced studies of the relationship between mass, acceleration and force acting on objects today.

Reference materials

_{Newton’s second law: F = ma}

_{Newton's Second Law}