Newton's Laws Of Motion

If a wooden block and a block of ice stay at rest on a floor without being pushed, both of term will stay motionless. However, when they are pushed by the same magnitude of forces so that they finally move, the ice block will slide further than the wooden block. How could it be? Why don't the Why don't the wooden block and the ice block move when no push was done? Why does the ice block tend to keep moving when the push is removed?

A body moves due to the presence of force working on it. Because of the given push, the wooden block and the ice block can move before they finally stop. The relationship between the force and the motion is studied in a branch of physics called dynamics.

A) Newton's Laws of Motion

1. Newton's First law

Basically, all objects tend to keep their motion state. If they are initially at rest, they tend to stay at rest. If they are moving, they tend to keep on moving. This property is called inertia.

It takes three men to move the car from its rest condition. But, when it is already moving, it only takes one man to keep the car move, while the car move. While the car is at rest, it tends to stay at rest so that we need a great amount of force to strive against its inertia in order to make it move. On the other hand, when the car is already moving, it tends to keep its motion state. And during that time, it only takes a smaller force to keep the car move compared with the force needed to make it move from its rest condition.

Newton's First Law states that:

if the 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 follows
𝞢 F = 0   ...... (1)

2.  Newton's second Law

What happened if the magnitude of the resultant force working on an object is not zero? In that case, the velocity of the object will change. It will increase if the direction of the resultant force is the same as the direction of the velocity of the object. On the contrary, the velocity of the object will decrease if the direction of the resultant force is opposite to the direction of the velocity of the object. The relationship between the resultant force and the acceleration can be explained by using Newton's second law, which states that:

If the resultant of forces working on an object is not zero, then the object will experience an acceleration in the same direction with the resultant force.

Mathematically, the Newton's second law can be written as follows.
𝞢 F = ma  or  F = ma   ..... (2)
where D is the magnitude of force, m is the object's mass, and a is the acceleration experienced by the object.

3. Newton's Third Law

If we press a wooden block with our finger, we will feel hurt. Why? The pain is actually caused by the force that is exerted by the wooden block. The magnitude of force exerted by the block to our finger is the same as the magnitude of force exerted by our finger to the block. The harder we press the block, the more hurt our finger will be. This phenomenon shows the existence of action-reaction force. Because the finger exerts a force on the block, the block will also exert a force on the finger with the same magnitude but in opposite direction. The force exerted by the finger is called an action, whereas the force exerted by the block is called reaction. This phenomenon is expressed in the Newton's third law, which states that:

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

Faction = - Freaction

The negative sign indicates that Faction and Freaction are in opposite direction. The forces of action and reaction are always the same, in opposite direction, at the same incident point, and working on two different objects.

In Figure 2.3 F₁ is the force exerted by the hand on the rope. And the reaction force F₁ is the force exerted by the rope on the hand. Vector F₂, shows the force exerted by the hand on the block, and the reaction F2, shows the force exerted by the block on the hand.

4. Analysis Of Object's motion in the absence of friction force

every object obeys the Newton's laws of motion. We will discuss several examples of the motions of objects in our daily lives. In this discussion, the friction that influences the motion of an object is neglected.

a. An object Moving on A Flat Plane

An object on a flat plane is given a horizontal force so that its acceleration becomes a= F/m

b. 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 (a) can be determined by using the following equations.

∑F = ma  → w sin Ө = ma à mg sin Ө= ma

Therefore, the magnitude of acceleration of the object on an inclined plane with elevation angle of  Ө is

a = g sin  Ө

Where g is gravitational acceleration.

c. Two Objects on a Pulley

Block-1 (which mass is ) by a string through a pulley. In this case, the string's mass and the friction caused by the pulley. In this case, the string's mass and the friction caused by the pulley is neglected. Block-1 moves to the right with acceleration experienced by block-2 that moves downward. The force working is horizontal direction is the string's tension T. Whereas in a vertical direction, it works the string;s tension T and the weight force of block-2 (W₂).

Exercise 2.1

1. An object with mass of 50 kg is initially at rest. It is then accelerated to reach a velocity of 20 m/s within 5 seconds. What is the magnitude of force that accelerated the object?

2. Two object m₁ = 10 kg and m₂ = 15 kg, are set as shown in the picture. What is the acceleration of each object? (g = 10m/s²)

B ) Friction Force 

We way see some cleats at the bottom soccer shoes. They are attached for protecting the player who wears it from sliding. The cleats will increase the friction between the shoes and the surface of the soccer field. Meanwhile, the frictions among the engine parts of a car are always tried to be minimized by using lubricant oil. Therefore, some frictions are useful (advantageous), while some others are disadvantageous. The friction force is the force that occurs when two objects contact with each other. It is divided into two: static friction and kinetic friction forces.

1. Static Friction Force

Static friction force fs occurs between the contact surfaces of two objects when the external force that works on the system does not cause relative motion toward each other. A block with mass m is pulled by a force F on a rough plane. IF the block is not moving yet, it means that there is a force F. The magnitude of the force is equal to F but the direction is opposite to the direction of the force F. That force is what we called static friction force (fs).

If the force F keep on increasing, then the static friction force is also increasing until at a certain time it reaches its maximum value, that is Fsmax. The maximum value of the static friction force is proportional to the coefficient of static friction (μ_s) between the block and the plane surface and the normal force of the block (N). It can be written as (F_smax) = μ_s N. The magnitude of the static friction force ranges from zero to its maximum value so that it can be written. 

0 ≤ fs ≤μ_s N

The block is said to be about to move it the magnitude of the external force F is exactly the same as the maximum value of the static friction force, or it is expressed by F = F_smax.

2. Kinetic Friction Force

Kinetic friction force exits between the contact surfaces of two objects when there is relative motion toward each other. If the force F keeps on increasing so that it exceeds the magnitude of the maximum static friction force, then the block will move eventually. Because the moving block and the surface of the rough plane still contact with each other, then there must be friction force working on the system. However, that friction force is not static friction force, it is the kinetic friction force (f_k).

The magnitude of the kinetic friction force is proportional to the coefficient of kinetic  (μ_k) between the block and the surface of the rough plane and the normal force of the block (N). It is formulated

f_k = μ_k N

Newton

Related Posts