Work, Energy, and Simple Machines

REVISION SUMMARY: Work, Energy, and Simple Machines (Chapter 7)

1. Chapter at a glance

• Work done by a constant force on an object equals force applied multiplied by displacement in the direction of the force.
• Work done on an object appears as a change in its energy (work-energy theorem).
• Kinetic energy is the energy an object possesses due to its motion; potential energy is the energy stored due to deformation or relative position of objects in a system.
• When only gravitational force acts, the mechanical energy (KE + PE) of an object remains constant.
• Power measures the rate at which work is done.
• Simple machines (fixed pulley, inclined plane, lever) change the magnitude or direction of force applied but do not reduce the total work done.

2. Definitions and laws (exactly as framed in NCERT)

• Work done on an object by a constant force = force applied × displacement in the direction of the force.
• 1 J = 1 N × 1 m (or 1 J = 1 kg m² s⁻²).
• Work-energy theorem: work done on an object = change in its energy.
• The energy possessed by an object due to its motion is called kinetic energy.
• The energy stored by an object as a result of its deformation or in a system of objects due to their relative positions is called the potential energy.
• The sum of the kinetic energy and the potential energy of the object is called its mechanical energy.
• Power is defined as the rate at which work is done: average power P = W/t.
• Mechanical advantage = load/effort.

3. Important diagrams and activities

• Fig. 7.2 (lifting bags): Shows work done is proportional to both the force applied and the displacement.
• Fig. 7.3: Work done by a constant force in horizontal or vertical direction.
• Fig. 7.4 (force-displacement graph): Area under the graph equals work done.
• Fig. 7.5 (pushing a wall): Demonstrates work = 0 when displacement s = 0.
• Fig. 7.6 (carrying a box): Demonstrates work = 0 when force is perpendicular to displacement.
• Fig. 7.7: Positive work (force and displacement in same direction) and negative work (opposite directions).
• Fig. 7.11: Derivation of kinetic energy using work-energy theorem.
• Activity 7.1 (ball dropped in sand from different heights): Shows potential energy increases with height above Earth’s surface.
• Activity 7.2 (simple pendulum): Demonstrates conservation of mechanical energy (bob reaches nearly same height on both sides).
• Fig. 7.23–7.25 (pulley): Shows how a fixed pulley changes direction of effort; movable pulley system can give mechanical advantage > 1.
• Fig. 7.26–7.28 & Activity 7.3 (inclined plane): Shows effort decreases as length of incline increases for the same height.
• Fig. 7.31–7.34 & Activities 7.4–7.5 (lever): Shows effort × effort arm = load × load arm; mechanical advantage = effort arm/load arm.

4. Common misconceptions and exam pitfalls

• Believing work is done whenever force is applied (NCERT explicitly states work = 0 if s = 0, e.g., pushing a wall, or if force is perpendicular to displacement).
• Confusing the sign of work: positive when force and displacement are in the same direction, negative when opposite.
• Assuming machines reduce total work done (they only change force or direction; total work remains the same, ignoring friction).
• Forgetting that kinetic energy depends on v² (doubling velocity quadruples KE).
• Using U = mgh indiscriminately (valid only near Earth’s surface).
• Not specifying the agency applying the force and the object on which work is done.
• Mixing up mechanical advantage with efficiency or assuming it reduces energy input.

5. Formula sheet

All formulas are to be used with consistent SI units. Work and energy are scalars.