Newton’s laws of motion

1. Newton’s first law states that: a body continues in its state of rest, or uniform motion in a straight line, unless acted upon by a resultant force. That is, a body will not move, change its direction of motion, or accelerate unless it is compelled to by some external force. Therefore a force can be defined as that which changes or tends to change the motion of a body upon which it acts.
2. Newton’s second law states that: the rate of change of momentum of a body is proportional to the resultant force applied to that body and takes place in the direction in which the force is applied
3. Newton’s third law states that: for every acting force there is an equal and opposite reaction force

From Newton’s second law of motion it is apparent that:

The applied force ∝ rate of change of momentum

The applied force ∝change in momentum/time

Thus if a force F causes a mass m to experience a change in velocity from v₁ to v₂ in time t, then:

F ∝ (mv₂–mv₁)/t

F ∝m(v₂–v₁)/t

F ∝ma where a =(v₂–v₁)/t

Therefore

F =ma ×constant

By choosing unit force (N), unit mass (kg) and unit acceleration (m/s²), the constant becomes 1 and:

F =ma

Example

A motor car of mass 4000 kg accelerates from 10 to 60 km/h in 10 s. Determine the applied force required to produce the acceleration.

v₂ =v₁+at      

Where:

v₂ =60 km/h=16.67 m/s

v₁=10 km/h=2.78 m/s

t =10 s

Then:

a =(v2-v1)/t

a =(16.67-2.78)/10

a =1.39 m/s²

Since:

F =ma

F= 4000 kg ×1.39 m/s²

F =5.56 kN