Force and Pressure: Motion

A. What is a Force?

A Force is an external push or pull acting on a body that changes or tends to change its state of rest, uniform motion, direction, or dimensions (shape/size).

• SI Unit: Newton ($\text{N}$). $1\text{ N}$ is the force required to accelerate a $1\text{ kg}$ mass at $1\text{ m/s}^2$.
• Gravitational Unit: Kilogram-force ($\text{kgf}$): $1\text{ kgf} = 9.8\text{ N} \approx 10\text{ N}$.

B. Classification of Forces:

1. Contact Forces: Require direct physical contact between interacting bodies.
   • Muscular Force: Force exerted by human/animal skeletal muscles.
   • Mechanical / Normal Force: Perpendicular contact force exerted by a supporting surface.
   • Frictional Force: Resisting tangential force opposing relative motion.
   • Tension Force: Restoring force transmitted through a stretched string or cable.
2. Non-Contact (Action-at-a-Distance) Forces: Act across empty space without physical contact.
   • Gravitational Force: Universal attractive force between masses ($F = \frac{G m_1 m_2}{r^2}$).
   • Electrostatic Force: Attractive or repulsive force between stationary electric charges.
   • Magnetic Force: Force exerted between magnetic poles or on moving charges.

A. Origin of Friction:

Even highly polished surfaces possess microscopic peaks (asperities) and valleys. When two surfaces touch, their asperities interlock and form microscopic cold welds. The force required to shear these junctions is Frictional Force.

B. Types of Friction (Hierarchy of Magnitudes):

• Static Friction: Self-adjusting frictional force preventing a stationary body from starting motion. Its maximum threshold is called Limiting Friction.
• Sliding Friction: Resisting force when one surface slides over another.
• Rolling Friction: Resisting force when a spherical or cylindrical object rolls over a surface (much smaller because the contact area is extremely narrow).

C. Modifying Friction:

• Increasing Friction: Grooving automobile tires, applying magnesium carbonate powder on gymnasts' hands, treading shoe soles.
• Decreasing Friction: Applying lubricants (oil, grease, graphite), installing ball bearings, polishing surfaces, streamlining aircraft and car bodies.

A. Definitions & Mathematical Formulations:

• Thrust: The total normal force exerted perpendicularly against a surface: $\text{Thrust} = F$ (Unit: Newton, $\text{N}$).
• Pressure ($P$): The thrust acting perpendicularly per unit surface area: $$\mathbf{P = \frac{\text{Thrust } (F)}{\text{Area } (A)}}$$
• SI Unit: Pascal ($\text{Pa}$): $1\text{ Pa} = 1\text{ N/m}^2$. Practical unit: $\text{bar}$ ($1\text{ bar} = 10^5\text{ Pa}$) and atmosphere ($1\text{ atm} = 1.013 \times 10^5\text{ Pa}$).

B. The Inverse Area Principle:

For a constant thrust force $F$:

• Small Area $\implies$ High Pressure:
  • A sharp knife has an extremely thin cutting edge ($A \to 0$), producing immense pressure with minimal hand force to slice vegetables cleanly.
  • Sewing needles and drawing pins have needle-thin tips to puncture fabrics and wood with light thumb pressure.
• Large Area $\implies$ Low Pressure:
  • School bags have broad shoulder straps to distribute the bag's weight across a larger surface area, reducing pressure on shoulders.
  • Camels walk effortlessly across soft desert sand because their wide, broad footpads distribute body weight, preventing them from sinking.
  • Skyscrapers and railway tracks rest on broad concrete foundations and wooden/concrete sleepers to prevent ground subsidence.

Motion is the continuous change in position of an object relative to a stationary reference frame:

1. Translatory Motion: Every particle of the body moves through the exact same distance in the same time.
   • Rectilinear: Motion along a straight line (e.g., a car driving on a straight highway).
   • Curvilinear: Motion along a curved trajectory (e.g., a stone thrown at an angle).
2. Rotatory Motion: A body moves about a fixed internal axis such that each constituent particle describes a concentric circle (e.g., spinning top, blades of a ceiling fan).
3. Oscillatory / Vibratory Motion: A body moves to-and-fro repeatedly about a central mean position (e.g., simple pendulum, guitar string).
4. Periodic Motion: Motion that repeats itself at strictly equal intervals of time (e.g., revolution of Earth around the Sun, heartbeat).