# Newton’s law of motion

**1. Definition of force**

Force is something that causes things to accelerate. In other words, force is something that moves, stops, or changes the direction of movement of an object. Force is a vector quantity, therefore, has a magnitude and direction. The force symbol is F (Force). F is a general symbol of force. There are several types of forces and not all forces have the symbol F. The international system unit is kg m/s2 aka Newton.

**2. Definition of the net force**

The resultant force (ΣF) is the sum of all the forces acting on an object. Force is a vector quantity so the total force is calculated based on the vector addition rule.

The total force = 10 Newton, the direction of the total force to the right.

The total force = 8 Newton, the direction of the total force to the right.

The total force = 0

The total force = 0

**3. Newton’s laws of motion**

Newton’s laws of motion are the laws of physics about the motion of an object proposed by the English physicist, Isaac Newton.

**3.1 Newton’s First Law**

Newton’s First Law states that every object that is at rest to remain at rest or that every object that is moving straight at a constant speed will continue to move straight at a constant speed if the total force acting on the object is zero.

ΣF = 0

This equation is a mathematical statement from Newton’s first law.

See an object around you, such as a table or stone or any object. A table that is at rest will remain rest if not moved or not given an external force such as a push or pull. Is there no force that works on tables or rocks or objects that are at rest? There is a force acting on the object, but the sum of all the forces acting on the object or the total force is zero. The force acting on objects that are still on the surface of planets like the earth is gravity (w) and normal force (N). The direction of the gravity force perpendicular to the center of the earth, the direction of the normal force is perpendicular upward. The magnitude of these two forces is the same but they have the opposite direction, so the total force is equal to zero.

What about things that are moving straight with constant speed? To clarify this problem, suppose you push an object, for example, a piece of metal, on the surface of the floor. After being pushed, the metal slowed and stopped because of friction. For metal pieces to move farther or longer then you have to smooth the floor surface and surface of the metal plate. If the floor surface is smooth and there is no friction, the metal plate will continue to move and not stop. Is there no force acting on the metal plate that is moving on the surface of the perfect smooth floor? There are forces that work on metal plates, namely the force of gravity and the normal force. Both of these forces work in a vertical direction and do not affect the movement of metal plates in the horizontal direction if the floor is smooth.

**3.2 Newton’s Second Law**

Newton’s Second Law states that if the total force acting on an object is not equal to zero then the object will accelerate. The magnitude of the acceleration is proportional to the magnitude of the total force and inversely proportional to the mass of the object. The direction of acceleration is the same as the direction of the total force.

ΣF = m a

ΣF = total force (kg m/s^{2}), m = mass (kg), a = acceleration (m/s^{2})

Equation 1.2 is a mathematical statement from Newton’s second law.

If the acceleration is equal to zero (a = 0) then equation 1.2 changes to equation 1.1. So Newton’s first law is a special case of Newton’s second law. Based on equation 1.2 it is concluded that the greater the force, the greater the acceleration. Conversely the greater the mass, the smaller the acceleration. The relationship between force, mass, and acceleration is better understood after you have conducted an experiment regarding this.

Sample problem 1:

Determine the magnitude and direction of the acceleration of objects based on the figure above…

Solution:

ΣF = m a

4 kg m/s^{2} = (1 kg) a

a = 4 kg m/s^{2 }: 1 kg = 4 m/s^{2}

The magnitude of acceleration = 4 m/s^{2}, the direction of acceleration to the right.

Sample problem 2:

Determine the magnitude and direction of acceleration based on the figure above …

Solution:

ΣF = m a

4 kg m/s^{2 }– 1 kg m/s^{2} = (1 kg) a

3 kg m/s^{2} = (1 kg) a

a = 3 kg m/s^{2} : 1 kg

a = 3 m/s^{2}

The magnitude of acceleration = 3 m/s^{2}, the direction of acceleration to the right.

**3.2.1 Weight (w)**

Weight is the force of gravity acting on a mass object.

ΣF = m a

w = m g

Equation 1.3 is the equation for calculating the weight of an object.

w = weight (kg m/s^{2}), m = mass (kg), g = acceleration of gravity (m/s^{2}). The magnitude of the gravitational acceleration (g) on the earth’s surface is 9.8 m/s^{2}. To simplify calculation, g is rounded to 10 m/s^{2}.

**3.2.2 Normal force (N)**

The normal force is the force acting on two objects that touch one another, in which direction of the normal force is perpendicular to the surface of the touch plane.

Observe objects that are still above the table surface. Force of gravity or weight also works on the object. Objects do not fall freely like fruit falling from a tree because there is a normal force. The weight (w) and normal (N) are the same but opposite directions so that the total force on an object is zero.

ΣF = 0

N – w = 0

N = w

**3.3 Newton’s Third Law**

Newton’s third law states that if object 1 gives force to object 2 then at the same time object 2 gives force to object 1. The two forces are the same but the direction of the two forces is opposite. One force is called action, another is called reaction.

F action = – F reaction

Equation 1.3 is a mathematical statement from Newton’s third law. The negative sign in equation 1.3 explains the direction of the force.

Experiment so that you better understand Newton’s third law. If you have a skateboard, push the wall while standing on a skateboard. After pushing the wall, the skateboard moves backward. The direction of your force forward, while the direction of the skateboard backward.

This shows that the wall also enforces you. When you push the wall, at the same time, the wall also pushes you. Your push force works on the wall while the push force of the wall works on you. Both forces are in the same but in opposite direction. You can call one force action and another as a reaction.

Another experiment that can be done is to blow a rubber balloon and after the rubber balloon expands because it is filled with air, release the balloon. After being released, the balloon is “flying”. The direction of balloon motion is opposite to the direction of air exit from the balloon. How to explain this?

When the balloon’s mouth is released, the balloon pushes the air out. At the same time, the air also pushes the balloon. The air push force causes the balloon to fly. The force of the balloon works on the air, the force of the air works on the balloon. The two forces are the same but the direction is opposite.

Observe figure 2 and compare it to figure 3. The normal force acting on an object (N) is the force given by a flat surface, such as a table surface. At the same time, objects also give force to the table surface (N ‘). Both of these normal forces (N and N ‘) have the same magnitude but are in opposite directions and work on different objects. Unlike w and N which have the same magnitude and work on the same object. So N and N ‘are action-reaction forces.