Newton’s Second Law of Motion

Key Concepts:

• Newton’s second law of motion
• Relate force, mass and acceleration

Introduction: 

In this session we are going to learn about second law of motion of Newton. 

Explanation: 

Newton’s second law of motion 

Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which force acts. Force is equal to the product of mass and acceleration. 

F = ma 

Few of the applications are: 

• A fielder pulls his hand backward while catching a cricket ball coming with a great speed, to reduce the momentum of the ball with a little delay. This reduces the effect of the force exerted by the ball on his hands. 
• Seat belts prevent injuries when brakes are applied in a fast-moving car. A car has a large momentum due to its large velocity, which is reduced to zero in a very short time, hence provided with seat belts.  

• For athletes, during long and high jump, sand bed or cushioned bed is provided to allow a delayed change of momentum to zero to prevent the athletes from being injured due to rapid change in momentum to zero. 
• A karate player breaks slab of bricks in a single blow as when hands move they carry velocity and when they touch slab the velocity is reduced to 0 in a very short time. Hence, the force exerted is very high and the slab breaks in a single blow. 

 

One Newton: 

One Newton is defined as that force necessary to provide a mass of one kilogram with an acceleration of one meter per second per second squared. 

1 Newton (N) = 1kg × 1m/s² 

1N = kg m/s² 

Derivation of Second Law of Motion 

Let the mass of a moving object be m and F be the force acting on it. 

Let the velocity of the object change from u to v in the interval of time t. 

Momentum = p = Mass × velocity  

Initial momentum = mu 

Final momentum = mv 

Change in momentum = mv – mu = m(v–u) 

Rate of change of momentum = m(v–u)/t  

Force ∝ Rate of change of momentum 

F ∝ m(v–u)/t 

F ∝ ma (because a = (v–u)/t) 

F = kma,  

where k is the constant of proportionality 

F = ma 

(k = 1, m = 1kg, a = 1m/s²) 

Questions and Answers 

Question 1: How much force is  needed to produce an acceleration of 20 m/s² in a body of mass  500 g? 

Answer: 

m = 500 g = 0.5 kg 

a  = 20 m/s² 

F = ? 

F = m × a  

   = 0.5 – 20  

  = 10 N  

Question 2: A body of mass 5 kg is moving  with a uniform velocity of 10 m/s. It is acted upon by a force of 20 N. What will be its acceleration?  

Answer: 

M = 5 kg 

u = 10 m/s, F = 20 N  

F = ma 

a =  F/m 

    = 20/5 

    = 4 m/s² 

Question 3: A body of mass 2 kg is kept at rest. A constant force of 6 N starts acting on it. what will be its acceleration? 

 

Answer: 

m = 2 kg 

u = 0 m/s 

F = 6 N 

a = F/m  

   = 6/2 

   = 3 m/s²  

Summary:

• Newton’s second law of motion – “The rate of change of momentum of a body is directly
  proportional to the applied force and takes place in the direction in which force acts.”
• F = ma where F is the force applied, m is the mass of the object and a is the acceleration
  of the object
• One Newton is defined as that force necessary to provide a mass of one kilogram with an
  acceleration of one meter per second per second.