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Newton’s Laws of Motion
As already discussed in the previous topic,motion of objects are caused by unbalanced forces that act on the objects. Therefore, forces are related to motions of objects.

This was discovered by Sir Isaac Newton ( 1642 – 1727 ). He stated three laws of motion .
Newton’s First Law Of Motion:
Newton’s first law of motion states that an object will continue in its state of rest or motion in a straight line unless it is acted upon by an external force.
Inertia:
Inertia is the unwillingness of an object in motion to stop moving or an object at rest to start moving.
Inertia simply means unwillingness. Every object is unwilling to do other wise apart from what its is doing at the moment. Inertia is inherent in every object and is a property of very matter. 
Mass:
Mass is the quantity of matter that is contained in an object. The more the quantity of matter that is contained in an object, the larger the mass of the object. Mass is measured in kilogram ( kg ). It is a scalar quantity.
Inertial Mass:
Inertial mass is a property of a matter which represent a resistance that the resistance f the object to any type of force.

Weight:
Weight of an object is the gravitational pull on the object. Or It can be defined as the force that is acting on the object due to the earth gravitational pull. Weight is measured in Newton. It is a vector quantity.

Relationship Between Inertia And Mass:
Mass of an object is the quantity of matter in the object. Mass of an object is a measure of the inertia of the object. The mass of an object determines the amount of inertia / resistance that the object will offer to a force that act on it and try to change its state. The more the mass of an object, the more the inertia of that object  will be, the more the resistance and the larger the force required to change the state of rest of the object or uniform motion .
Relationship Between Mass And Weight:
The relationship between mass and weight is the formula that connect mass and weight. This formula is used in calculations, to either calculate the weight of a given mass of object or to calculate the mass of a given weight.
The formula is :     weight = mass X acceleration due to gravity
                                 Weight = mX g
Worked Examples:
1. Calculate the weight of a mass 2.6gram.
      Data given in the question: 
      Mass = 225g = 225 /1000 = 0.225 kg.
       Formula:   weight =  mass  X  acceleration due to gravity
       Substitution:      weight = 0.225 X 10.  

weight = 2.25N
2. What is the mass of object whose weight is 35N? ( g = 10 m/s² )
        Data given in he question:
        Weight = 35 N, g = 10 m/s²
         Formula:  weight = mass * acceleration due to gravity
        Substitution:  35 = mass X 10
       Make mass the subject:    mass = 35 / 10.

mass = 3.5 kg 

Significance Of Newton’s First Law Of Motion:
The significance of Newton’s first law of motion is that, Newton’s first law  of motion make us to understand that inertia ( unwillingness ) is present in every object. 
Short Coming Of Newton’s First Law Of Motion:
Though Newton’s first law of motion make us to know that inertia is inherent in every object and also explain what force does on an object. Newton’s first law of motion does not suggest how force should be measured.

Newton’s Second Law Of Motion:
Newton’s second law of motion states that the rate of change of momentum is directly proportional to the force that caused the change and take place in the direction of the force.
The formula that connect force and mass is as stated below:
           Force = mass of object  X acceleration of the object 
          F = m X a
 Example 1:
1. Calculate the magnitude of the force that act on 12kg mass such that its acceleration is 1.75 m/s².
          Solution:
          Data given in the question:
        Mass = 12kg, acceleration = 1.75 m/s², force = ?
        Formula:  force = mass  X acceleration
      Substitution:    force = 12 X 1.75 
      Force = 21 Newtons
2. Given that 35 N force act on 2.6 kg mass. If the velocity of the object is 0.25 m/s, determine the acceleration of the  object.
          Solution:
Force = 35 N,  Mass=2.6 kg and velocity = 0.25 m/s
Formula:   Force = mass X acceleration
Substitution:  35 = 2.6 X  acceleration
Make acceleration the subject:    acceleration = 35 / 2.6
Acceleration = 13.46 m/s
3. An unbalance force of 25 N act on a 8.0 kg mass. What  acceleration does it gives to the mass?
Solution:
         Mass = 8.0 kg, force = 25 N, acceleration = ?
          Formula:  force = mass  X  acceleration
          Substitution:  25 = 8.0  X  acceleration 
          Make acceleration the subject:    acceleration = 25 / 8.0
          Acceleration = 3.13m/s²
Formula Of Newton’s Second Law Of Motion:
From the above statement of Newton’s second law of motion, the formula Newton’s second law of motion is obtained as follow:
              Mathematically,
          Force is directly proportional to rate of change in momentum
          Force ∞ rate of change in momentum
          Force ∞ change in momentum / time 
         Force ∞ (MV – MU) / time
       Factorize m:       Force ∞ m (  v – u ) / t
     Recall that acceleration

a = (final velocity v – initial velocity u) / time t
                       a = (v – u) / t
Substitute for a in the above equation: force = mass * acceleration
              Force ∞ mass = acceleration
Replay the proportional symbol with k:

• force  = k X m X a.
  If constant k is 1, then the formula will become,
                      Force = ma

or

• acceleration = force / mass
• or
• mass = force / acceleration

Examples:
1.  N object of mass 950g is pulled along a tarmac by a horizontal force of 20 N. A frictional force of 6 N opposed the motion . what is e acceleration of the stone?
             Solution:
             Data given in the question: 
           Mass of stone = 950 g = 950 / 1000 = 0.95 kg, force = 20 N , 
            frictional force = 6 N, 
Note: 
         Since friction force is present to oppose the motion of the object,     the force that moves the object or the effective force will be the difference between the give force and the frictional force.

Therefore,
          Effective force = force – friction force
         Effective force = 20 – 6 = 14 N 
       Formula:   force = mass X acceleration
       Substitution:      14 = 0.95  X  acceleration
        Make acceleration the subject:    acceleration = 14 / 0.95
                                 Acceleration = 14.74 m/s² 
2. A ball of mass 3 kg that is moving t a velocity of 26m/s is suddenly hit by a force of 6 N for 0.05 second. Find the new velocity of the object.
            Solution:
            Data given in the question:
         Mass = 3 kg, velocity =26 m/s, force = 6N, time = 0.05 second
Note:  Velocity of 26 m/s is given in the question and we  asked to calculate the new velocity of he object. That velocity is the initial velocity u, of the object while the new velocity that we are asked to calculate is the final velocity v, of the object.
              Formula:        

  Force = ( MV – MU ) / t
                               Force = m ( v – u ) / t
            Substitution:       6 = 3 ( v – 26 ) / 0.05
             Cross multiply:    6  X 0.05 = 3 ( v – 26 )
                                      0.3 = 3 ( v – 26 )
.                                     0.3 / 3 = v – 26
                                    0.10 = v – 26
             Make v the subject:    v = 0.10 + 26
                        V = 26.10 m/s