Science: Class 9 — Chapter 7: Work, Energy, and Simple Machines

7.1 Work Done by a Constant Force

7.1.1 Scientific Definition of Work

Work Done: Defined as the product of the force applied on an object and its displacement in the direction of that force (W = F × s).
Joule (J): The SI unit of work. One Joule is the work done when a constant force of 1 Newton (N) displaces an object by 1 metre (m).
Graphical Method: For both constant and variable forces, the work done equals the area under the force-displacement graph.

7.1.2 Conditions for Zero Work

Zero Displacement: If the displacement (s) is zero, no work is done (e.g., pushing a rigid wall).
Perpendicular Force: If the force acts perpendicular to the direction of displacement, the work done is zero (e.g., carrying a box horizontally).

7.1.3 Positive and Negative Work Done

Positive Work: Occurs when the displacement is in the same direction as the applied force (e.g., pushing a wheelchair).
Negative Work: Occurs when the displacement is opposite to the direction of the applied force (e.g., a goalkeeper applying force to stop a football).

7.2 The Work-Energy Theorem

7.2.1 Relationship Between Work and Energy

Energy: The capacity to do work, sharing the same SI unit, the Joule (J).
Work-Energy Theorem: States that the work done on an object is equal to the change in its energy (Work = Change in Energy).
Energy Transfer: Energy can be transferred via mechanical work, heat, radiation, electricity, sound waves, or nuclear reactions.

7.3 Forms of Energy

7.3.1 Primary Types of Energy

Mechanical Energy: Energy due to the motion or position of objects.
Thermal Energy: Heat energy associated with molecular warmth.
Chemical Energy: Energy stored in fuels and food chemical bonds.
Electrical Energy: Energy related to the position or movement of charges.
Nuclear Energy: Energy stored in atomic nuclei.

7.4 Mechanical Energy

7.4.1 Kinetic Energy

Kinetic Energy (K): The energy possessed by an object due to its motion, expressed mathematically as K = ½ mv².
Velocity Dependence: If the velocity of an object doubles, its kinetic energy increases fourfold.

7.4.2 Potential Energy

Potential Energy (U): Energy stored as a result of deformation (e.g., a stretched rubber band) or due to the relative positions of objects in a system.
Gravitational Potential Energy: Energy possessed by an object raised to a height near Earth's surface, calculated as U = mgh.

7.4.3 Conservation of Mechanical Energy

Total Mechanical Energy: The sum of the kinetic and potential energy of an object.
Conservation Principle: In the absence of external resistive forces (like friction), total mechanical energy remains constant (K + U = Constant).

7.5 Power

7.5.1 Rate of Doing Work

Power (P): The rate at which work is done, defined as P = W / t.
Watt (W): The SI unit of power. One Watt equals 1 Joule per second (1 J s¹).
Horsepower (hp): A historical non-SI unit of power, where 1 hp = 746 W.

7.6 Simple Machines

7.6.1 Machine Fundamentals

Simple Machines: Devices that make work easier by changing the magnitude or direction of an applied force, without reducing total work.
Effort: The force applied to the machine.
Load: The force/resistance to be overcome.
Mechanical Advantage (MA): The ratio of load to effort (MA = Load / Effort).

7.6.2 Pulley

Fixed Pulley: Changes direction of the effort force but maintains a mechanical advantage of 1.
Movable Pulley: Provides a mechanical advantage greater than 1, reducing the required effort.

7.6.3 Inclined Plane

Inclined Plane: A slanted surface used to ease lifting. Its mechanical advantage is given by MA = L / h.

7.6.4 Lever

Lever: A rigid bar rotating around a fixed point called the Fulcrum.
Law of Lever: Balanced when effort × effort arm = load × load arm.
Class I Lever: Fulcrum is in the middle (e.g., seesaw, scissors).
Class II Lever: Load is in the middle (e.g., bottle opener, wheelbarrow).
Class III Lever: Effort is in the middle (e.g., tongs, tweezers).