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).