Behind best catches is Newton: The Second Law of Motion

Newton’s first law of motion talks about the motion of an object acted upon by balanced forces - there is no acceleration (same state of motion or rest is continued). Newton’s second law talks about the motion of an object acted upon by unbalanced forces (when there is an individual force that is not being balanced by a force of equal magnitude and in the opposite direction) - there is acceleration.  

Linear momentum 

Linear momentum is defined as mass in motion along a straight line path. Since every object has mass, every object in motion has momentum (has its mass in motion). Mathematically, it is defined as the product of mass and velocity - p=mv where p is momentum, m is mass and  v is velocity. Thus the amount of momentum an object has is directly proportional to its mass and velocity (which makes sense from the definition of momentum as the more the mass, the more the mass in motion and the more the velocity, more is the motion of the mass!). 

Statement and formula 

Newton’s second law states that the rate of change of momentum of a body is directly proportional to the applied force and the change in momentum takes place in the direction of the applied force. 

F ∝ Δp⁄Δt 

F = kΔp⁄Δt 

F = kΔmv/Δt = kmΔv/Δt (if mass is constant-which is usually the case)

 F = kma where k is a constant and a is acceleration 

If we take the unit of force as 1 N the value of the constant is 1. This is because 1 N is defined as the force required to produce an acceleration of 1m/s² in an object of 1kg. So according to F=kma, 1N=k(1kg)(1m/s²) thus k=1. The unit of F,m and a are taken such that the value of k is always 1. If m is in grams, acceleration is taken in cm/s2 and force in dyne so that k=1 (1 dyne is the force required to produce an acceleration of 1cm/s² in an object of 1g so 1dyne=k(1g)(1cm/s²)). 

Thus F=ma

Consequences of the law 

• Concept of inertia 

It explains how mass of a body is a measure of inertia of that body in linear motion (mass∝inertia). Since F = ma, a = F/m. From which we can say that greater the mass of a body, smaller is the acceleration (smaller change in motion) produced in it by a given force and hence greater will be its inertia (more tendency to continue the same state of motion). 

• Measurement of force

The formula F = ma helps us find force easily by knowing the mass and acceleration (change in velocity in given time).

• Consistency with first law 

F = mΔv/Δt

 If Δv = 0 then F=0 which implies that a body continues motion with the same velocity if no external force acts on it. This is exactly Newton’s first law.

Impulse 

The term impulse is used to refer to fast-acting force or “impact”. It is the measure of the action of a large force acting for a short duration of time to produce a finite change in momentum. The same impulse or change in momentum can be produced by applying a small force for a long duration of time. Impulse = Δp = FΔt. Impulse can be defined as the product of average force (we assume the force is constant in the time interval) and the time interval for which the force acts on the body. It is represented by the symbol J. 

Why does a cricketer move his hand backwards while catching a ball? When a cricketer stops a ball an impulse acts on their hand because there is a change in momentum of the ball. The change in momentum is due to the change in velocity from an initial value (say u) to 0 (as the ball stops). Change in momentum is equal to final momentum - initial momentum which is 0 - mu = -mu (m being the mass of the ball). Here the negative sign indicates the direction of change in momentum is opposite to that of initial motion (as momentum is decreasing). 

 Withdrawing their hands increases duration of impulse acting on them. Thus force acting on their hands is reduced (F∝1/Δt when J is constant). This is really important as it prevents injuries. Thus Surya didn’t forget it even in one of the trickiest catches in the World Cup.  

In hammering a nail we apply a large force quickly, generating a large impulse (J∝F). Thus there is a large change in momentum (velocity of the nail increases greatly) which drives it into the wood.  

Real law of motion 

Newton’s second law is called so as the first and third laws are contained in it. We already saw how Newton’s first law is consistent and can be derived from his second law. 

Newton’s third law can be derived using the law of conservation of momentum which is based on Newton's second law. This will be discussed in the next blog…

Conclusion 

To conclude, Newton’s second law states that the rate of change of momentum of a body is directly proportional to the applied force and the change in momentum takes place in the direction of the applied force. It helps quantify force by relating it to mass and acceleration. This law is known as the real law because the other laws are contained in it.  It explains the relation between inertia and mass and the impact of a force in an interval of time. 

Answers to the questions in the previous blog-:

Ans   0 N. An object in motion will maintain its state of motion. The presence of an unbalanced force changes the velocity of the object.

Ans   The large mass of the bull means that the bull has a large inertia. Thus, Ben can more easily change his direction of motion while the bull has extreme difficulty changing its direction of motion (inertia of direction ). Thus the bull will slow down.

Ans   C. must not be accelerating.

An object having balanced forces definitely cannot be accelerating as when no net force acts on an object it continues to be in its state of motion or rest. It resists change in velocity - it resists acceleration.