Work, Energy and Power

The One Thing

Work describes energy transfer by a force through displacement; the net work changes an object’s kinetic energy. Conservation of energy and momentum then provides the framework for analysing power, mechanical-energy changes and collisions.

Reactions, Processes and Experiments

Key Terms

• Work: Energy transferred when a force produces displacement. For a constant force, W = F s cos theta, where theta is the angle between force and displacement.
• Positive Work: Work done when a force has a component in the direction of displacement, such as gravity acting on a falling object.
• Negative Work: Work done when a force has a component opposite to displacement, such as friction acting on a moving block.
• Zero Work: Work done when there is no displacement or when the force is perpendicular to displacement, as in uniform circular motion for centripetal force.
• Kinetic Energy: Energy possessed by an object because of its motion: K = 1/2 mv^2.
• Potential Energy: Stored energy due to position or configuration. Near Earth’s surface, gravitational potential energy is U = mgh.
• Work-Energy Theorem: The net work done on an object equals its change in kinetic energy: W_net = Delta K = K_f - K_i.
• Conservative Force: A force whose work depends only on the initial and final positions, not on the path followed. Gravitational and elastic forces are examples.
• Non-Conservative Force: A force whose work depends on the path. Friction is a common example because it converts mechanical energy into heat.
• Mechanical Energy: The sum of kinetic and potential energies: E = K + U.
• Conservation of Mechanical Energy: When only conservative forces act, the total kinetic and potential energy remains constant: K_i + U_i = K_f + U_f.
• Power: The rate at which work is done or energy is transferred. Average power is P_avg = W/t; instantaneous power is P = dW/dt = F dot v.
• Collision: A short-duration interaction between objects during which large forces act and momentum is exchanged.
• Momentum Conservation: In an isolated system with no external net force, total linear momentum remains constant: p_initial = p_final.
• Elastic Collision: A collision in which both momentum and total kinetic energy are conserved.
• Inelastic Collision: A collision in which momentum is conserved but kinetic energy is not conserved.
• Perfectly Inelastic Collision: A collision in which the objects stick together after impact. Momentum is conserved, but kinetic-energy loss is maximum for the given initial conditions.
• Coefficient of Restitution: The ratio of relative speed of separation to relative speed of approach along the line of impact: e = relative speed of separation / relative speed of approach.

Easily Confused

• Positive work vs negative work: Positive work has a force component in the direction of displacement; negative work has a component opposite to displacement.
• Zero work vs negative work: Zero work occurs when displacement is absent or the force is perpendicular to it; negative work occurs when the force opposes displacement.
• Work vs power: Work measures energy transferred; power measures the rate at which the transfer occurs.
• Conservative force vs non-conservative force: Conservative-force work is path-independent and is zero around a closed path; non-conservative-force work depends on path.
• Mechanical-energy conservation vs total-energy conservation: Mechanical energy remains constant only when non-conservative forces do no net work, whereas total energy remains conserved because energy may be transferred or transformed.
• Momentum conservation vs kinetic-energy conservation: Momentum is conserved in an isolated collision, but kinetic energy is conserved only in an elastic collision.
• Elastic collision vs inelastic collision: Both involve momentum conservation in an isolated system, but only an elastic collision conserves total kinetic energy.
• Inelastic collision vs perfectly inelastic collision: In every perfectly inelastic collision the objects stick together; ordinary inelastic collisions need not have this outcome.
• Average power vs instantaneous power: Average power is P_avg = W/t over a time interval; instantaneous power is P = dW/dt = F dot v at a particular instant.
• Joule vs watt: A joule measures work or energy, whereas a watt measures power; 1 W = 1 J/s.
• Kinetic energy vs momentum: Kinetic energy is a scalar, K = 1/2 mv^2; momentum is conserved in isolated collisions and is represented by p_initial = p_final.

What Gets Asked

• Calculate the work done by a constant force using W = F s cos theta; marks are lost by using the full force instead of its component along the displacement.
• Determine whether work is positive, negative or zero in situations involving gravity, friction, centripetal force or a normal force; the key distinction is the angle between force and displacement.
• Apply the work-energy theorem using W_net = Delta K = 1/2 m(v^2 - u^2); the common error is confusing net work with the work done by one individual force.
• Use K_i + U_i = K_f + U_f for systems involving gravitational or elastic potential energy; this equation applies only when non-conservative forces do no net work.
• Compare processes or machines using P_avg = W/t or P = dW/dt = F dot v; completing the same work in less time means greater power, not greater work.
• Analyse collisions using momentum conservation and identify whether kinetic energy is also conserved; momentum conservation alone does not establish that a collision is elastic.