Application of Newton’s Laws

What are Forces?

Forces are the result of the interaction between bodies. In simple words, a force is the push or pull acting on an object. For example, you exert a force on a rope to pull an object, and the rope pulls the object.

Here, we need a transition between the definition of forces and Newton’s Laws. We also need a couple of examples of how to draw a force diagram.

The Law of Inertia

Newton’s first law of motion explains the relation between the force applied on an object and its motion.

The law states that:

An object continues to remain in a state of rest or of uniform motion in a straight line unless compelled by an external force to act otherwise.

This means that an object prefers to remain in a state of rest or uniform motion; in order to change the state it’s in you need to apply force to it. Further, an object will always resist the force applied to it. The property of an object to resist an external force is called inertia, and for this reason, Newton’s first law is called the law of inertia.

If you slide an object on a smooth floor with a given speed, the distance it moves depends upon the friction between the object and the floor. The smoother the floor, the greater the distance traveled by the object. The object eventually stops because of the external force of friction.

A force is required to change the velocity of a body. To understand this statement first recall from your study of kinematics that velocity is a vector with a magnitude (speed) and a direction. In the absence of a force, both speed and direction are constant. When a force acts on an object, it changes the speed, direction, or both of the objects.

There is no basic difference between an object at rest and an object in uniform motion; rest and uniform motion are relative terms. An object at rest with respect to one observer may have a uniform velocity with respect to another observer.

Newton’s Second and Third Laws (1 of 2)

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Newton’s Second Law

Newton second law states that:

The acceleration of an object is proportional to the applied force and takes place in the direction of the impressed force.

An object may experience a number of forces at any instant; one of them is the gravitational force, which always acts on an object in addition to other forces. The vector sum of all the forces acting on an object at any instant is known as the net force.

According to Newton’s second law, acceleration is proportional to the net force acting on an object and takes place in the direction of the net force. Therefore, if the force on an object is doubled, the acceleration will also be doubled. The relation between the force and acceleration of an object depends on the mass of the object; when the mass increases, the same force produces less acceleration.

Mathematically, Newton’s second law is expressed as:

F = ma Where: F = net force acting on an object m = Mass of the object a = acceleration of the object

Newton’s second law gives us a quantitative measure of the acceleration of an object when a force acts on it. While calculating the acceleration caused by a force, remember that the direction of acceleration is always in the direction of the force and its magnitude depends on the magnitude of the force and the mass of the object.

Because force and acceleration are vectors, Newton’s second law can be applied in any direction you want. The sum of the components of all forces in a given direction equals the product of the mass and the acceleration component in that direction.

Newton’s second law is also used to define the unit of force, Newton (N), as the force required to accelerate an object with a mass 1 kg by 1 m/s2. Thus, 1 N = 1 kgm/s2.

Inertial Reference Frames

An important consideration while applying Newton’s first and second laws is that these laws can be applied only by observers who are themselves not accelerating. For example, a person sitting in an accelerating car or riding a roller coaster cannot apply Newton’s first or second law. The person should be located in another frame of reference where he is not experiencing the force being analyzed. Frames of reference where Newton’s laws are applicable are called inertial reference frames.