Impact of Unbalanced Forces in the Second Law of Motion

• External Force Impact: The second law of motion specifies that an unbalanced external force on an object results in a change in its velocity, producing acceleration.
• Everyday Observations: A table tennis ball doesn’t hurt a player when hit, but a fast-moving cricket ball can. 
  • A stationary truck isn’t a threat, but a moving one can be fatal. 
  • A bullet, though small in mass, can be deadly when fired.
  • These observations highlight that the impact produced by objects depends on their mass and velocity.
• Greater Force Required: To accelerate an object, a greater force is necessary to achieve a higher velocity.
• Momentum: Newton introduced momentum, denoted by p, defined as the product of an object’s mass (m) and velocity (v):

 p = mv

• • Momentum has both magnitude and direction. Its direction coincides with the velocity. 
  • Its SI unit is kilogram-metre per second (kg ms-1).
  • An unbalanced force leads to a change in the object’s momentum.
• Example of a Car With a Dead Battery: A sudden push doesn’t start it, but a continuous push over time accelerates it to a speed that can start its engine. 
  • This implies that momentum change is influenced by both the force magnitude and the duration it’s applied.
• Momentum Change: The second law of motion posits that the rate of change of momentum of an object is proportional to the applied unbalanced force and occurs in the direction of this force.

The Mathematical Correlation: Exploring the Second Laws of Motion and Its Real-life Dynamics

• Initial Setup: Consider an object of mass m moving in a straight line. It has an initial velocity u and gets uniformly accelerated to velocity v over time t due to a constant force F.

• • • Initial momentum: p1 ​= mu
    • Final momentum: p2​ = mv

• Change in Momentum:

The change in momentum (Δp) ∝ p2 ​– p1​

                   Δp ∝ mv−mu

       Δp ∝ m × (v − u)

• Rate of Change in Momentum: The rate of change is momentum 

(Δp / t) ∝ m × (v − u) ​/ t

• Applied Force:

F ∝ m × (v − u)​ / t

F = km × (v − u) / t​

F = kma  

Here, k is the constant of proportionality

• SI Units: Unit of mass is kilogram (kg) and unit of acceleration is m/s2 

• • • One unit of force is defined such that k becomes one. Hence, 1 unit of force = k × (1kg) × (1ms -2).
  • Therefore, F = ma (which is the mathematical representation of the second laws of motion). Newton (N) is the unit of Force. 

• Real-life Observations:

• • • Catching in Cricket: A cricket fielder pulls their hands back while catching a ball to increase the time taken for the ball’s velocity to reduce, decreasing the ball’s acceleration and impact.
    • High Jump Landing: In a high jump event, athletes fall on cushioned or sand beds to increase the time taken for their momentum to stop, decreasing the change in momentum and the force of impact.
    • Karate Ice Break: A karate player’s ability to break a slab of ice in one blow can also be explained using the second laws of motion.

• Relation with First Laws of Motion:

• • The first law (i.e. objects remain in their state of motion or rest unless acted upon by an external force) can be derived from the second law’s mathematical expression.
  • Given F = ma, if F = 0, then v = u for any time t. If the object starts at rest (u = 0), it will remain at rest (v = 0).

Balancing Forces: Exploring the Dynamics of Newton’s Third Laws of Motion

• Overview: The third laws of motion deals with forces exerted by two objects on each other. When one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object.
• These forces, termed action and reaction forces, always act on different objects.
• Football Example: In football, when players collide, each feels the impact because they exert forces on each other. This interaction results in a pair of forces, not just one.

• Spring Balance Experiment: Using two spring balances connected together, if a force is applied to one balance, both show identical readings, but in opposite directions. 
  • Third Law Principle: This illustrates the third law as the force exerted by one balance on the other is equaled by the opposing force of the second balance on the first.
• Alternative Statement:This provides an alternative statement for the third law: “To every action, there is an equal and opposite reaction.” 
  • However, these forces act on two different objects.
• Walking Example: When someone tries to walk, they push the ground backwards. 
  • In return, the ground exerts an equal and opposite force forwards, propelling the person in the desired direction.

• Acceleration & Mass: While action and reaction forces are equal, they may not produce equal accelerations if the objects have different masses.
• Gun and Bullet Example: When firing a gun, the gun exerts a force propelling the bullet forward.
  •  The bullet exerts an equal force backward on the gun, resulting in the gun’s recoil. 
  • The gun, being much heavier than the bullet, has less acceleration than the bullet despite the forces being equal.

• Sailor and Boat Example: If a sailor jumps forward from a rowing boat, the boat moves backward. 
  • The forward force exerted by the sailor on the water or ground is countered by an equal backward force exerted by the water or ground on the boat.