Introduction to Power

Power Definition: Power (P) is the rate of energy transfer. P = dE/dt

Units of Power: The SI unit for power is the watt (W), which is joules per second (J/s).

Average Power: Average power (Pavg) is the total energy transferred (Delta E) divided by the time interval (Delta t) over which it occurred: Pavg = Delta E / Delta t or, if energy transfer is due to work, P_avg = W / Delta t.

Work Done in Example: For an object pushed at constant speed up a frictionless ramp, the work done is W = mgh, where m is mass, g is acceleration due to gravity, and h is the vertical height. The angle of the ramp does not affect the total work done.

Power in Example: The power dissipated depends on the work done and the time taken. For the same work (mgh), a shorter time interval results in higher power. P_avg = mgh / Delta t.

Kilowatt-hour (kWh): A kilowatt-hour is a unit of energy. It is defined as power (kilowatt) multiplied by time (hour). It is commonly used for billing household electricity consumption.

Types of Energy

Kinetic Energy (K): Energy associated with motion.

Potential Energy (U): Energy representing the potential to perform work.

Gravitational Potential Energy (Ug): Energy associated with an object's position in a gravitational field. Formula for change: Delta Ug = mg(Hfinal - Hinitial). Only the change in U_g is significant; dependent on chosen origin.

Elastic Potential Energy (UEL): Energy stored in a spring or elastic material when compressed or stretched. Relates to Hooke's Law: F = -kx (where x is displacement from equilibrium, k is the spring constant). Formula: UEL = 1/2 kx^2. x=0 is at the spring's natural equilibrium.

Internal Energy (Uinternal): Represents microscopic motion of particles (e.g., from friction, air resistance, collisions). Not a mechanical energy. Only the change in internal energy (Delta Uinternal) is considered. Always positive, as it represents energy added to the system's internal energy.