Analysis Of Object’s Motion In The Absence Of Friction Force

Every moving object obeys the laws of Newton on motion. We will discuss several examples of object motion in daily lives. In this discussion, the friction force that affects object’s movement is neglected.

- An Object Moving on A Flat Plane

An object on a flat plane is given a horizontal force so that its acceleration become.

a = F / m

- An Object Moving on An Inclined Plane

A Block is moving on an inclined plane. Base on the Newton’s second law, the acceleration of the block (c) can be determined by the following equations.

∑F = ma ,  w sin ϴ = ma , mg sin ϴ = ma

Thus the magnitude of the object acceleration on an inclined plane with angle ϴ is

a = g sin ϴ

where g is the gravitational acceleration.

Newton's Law of Motion (Newton's Third Law)

Action-Reaction

If we press a wood block with our fingers, we will feel hurt. Why is that? The pain is actually caused by the force from the wood to our fingers. The amount of force exerted to our finger is the same as the amount of force exerted by our fingers to the wood. The harder we push the wood the more hunt our fingers will be. This phenomenon indicates the existence if action-reaction. Because the finger exerts a force o the wood, the wood exerts a force on the figer with the same magnitude but in opposite direction. The force by the figer is called action, and the force by wood is reaction. This phenomenon is concluded in the Newton’s third law as follows.

If the first object exerts a force on the second object, then the object will exerts the same amount of force to the first object in the opposite direction.

F_action  = - F_reaction

The negative sign indicates that F_action and F_reaction are in opposite direction.

The forces of action and reaction are always the same, in opposing direction, at the same incident point, and work on two different objects.

The coupling force of action - reaction

Newton's Law of Motion (Newton's Second Law)

What happen if the resultant of force in an object is not equal to zero? If that’s the case, the object’s velocity will change. It will increase if the direction of resultant of force is in line with that of the object’s velocity. On the contrary, the velocity will decrease if the resultant of force is in opposite to that of the object’s velocity. The relationships of resultant of force and acceleration can be explained based on Newton’s law II, i.e.:

If the resultant of force working on an object is not equal to zero, the object will experience an acceleration, which direction is in line with that of the resultant of force.

Mathematically, Newton’s Second law can be written as follows

∑F = ma    or    F = ma

Where F is the magnitude of force, m is the object’s mass, and a is the acceleration experienced by the object.

A person playing snowboard esperiences acceleration due to external force working on her, e.g. her hands propelling force, the friction force, and the earth's gravity

Newton's Law of Motion (Newton's First Law)

Fundamentally, all objects tend to stay in their current position. If it is stand still, it wants to stay that way. If it is in motion, it wants to keep on moving. This property is known as inertia.

Newton’s first law states that:

If the force or resultant of force working on an object is zero, the object will stay at rest or keep on moving with constant velocity in a straight line.

This is also known as the law of inertia, which is mathematically written as pillows.

ΣF = 0

The tendency for a car to sit still when we push it is example of the inertia property of object.