Newton's Second Law: F = ma

Introduction

Force is an action that changes an object's velocity or shape. Newton's Second Law states that the acceleration of an object is directly proportional to the unbalanced force acting on it and inversely proportional to its mass. In other words, force, mass and acceleration are all closely connected to one another.

Balanced forces

There are many forces acting on objects on Earth, even stationary ones. When an object is stationary, two forces are acting upon it. One is the force of gravity. (Refer Chapter 5) This force pushes an object down towards the centre of the Earth. At the same time, the surface the object is sitting on pushes upwards with an equal force. This keeps the object from falling through the surface. In this case, the two forces acting upon the object are balanced because they act in opposite directions with the same magnitude.

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Unbalanced forces

When the forces are unbalanced (in other words, with different magnitudes), the object accelerates. An example of this is when a car accelerates from a stop. The driving force from the wheels of the car provides a forward force. This force then cancels out the forces that push in the opposite direction, such as air resistance and friction. (Refer Chapter 6) If the driving force is more than the forces of air resistance and friction, the car will accelerate forward.

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Newton's Second Law

An important distinction that Newton's Second Law makes in conjunction with his First Law (objects at rest tend to stay at rest, while objects in motion tend to stay in motion) is that force is not required for motion to continue. If an object is already moving, it does not require any force to continue moving. In fact, if no forces are imposed on a moving object, it will continue moving in the same direction and at the same speed until a force acts upon it.

Newton's Second Law can be expressed as these equations:

where F is the net (unbalanced) force, m is mass in kilograms and a is acceleration in m/s2. Force is measured in newtons (N). 1 N is enough force to accelerate 1 kilogram (kg) of matter 1 metre per second per second (m/s2).

From this equation, it can be seen that a larger force will create higher acceleration, while a larger mass will create lower acceleration. Evidence for this can be seen in daily life. Imagine pushing an empty cardboard box. It does not take much force to move an empty cardboard box. If you were to raise the box's mass by placing some bricks in it, however, it would require much more force to make the box accelerate from being stationary.

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