AP Physics C: Mechanics - Unit 3: Power and Energy Transfer

Power

The time rate at which work is done or energy is transferred.

Average Power

Total work done divided by the total time taken.

Instantaneous Power

The power output at a specific moment in time, defined as the derivative of work with respect to time.

Watt (W)

The SI unit for Power, defined as 1 Joule per second.

Energy

The capacity to do work.

Work

Measures the energy transfer caused by a force moving an object.

Scalar Quantity

A quantity that has magnitude but no direction.

Efficiency

The ratio of useful work output to the total work input, often expressed as a percentage.

Kinetic Energy (K)

The energy an object possesses due to its motion, defined as K = 1/2 mv^2.

Force Vector (F)

A vector representing the force applied to an object.

Velocity Vector (v)

A vector representing the instantaneous speed and direction of an object.

Dot Product

A mathematical operation that multiplies two vectors and returns a scalar, used to calculate power.

Change in Work (W)

The difference in work done over a period or interval.

Change in Energy (E)

The difference in energy state over a period or interval.

Angle (Theta, )

The angle between the Force vector and the Velocity vector in the context of power.

Graphical Analysis of Power

The method of interpreting data through the work vs. time and power vs. time graphs.

Work from Power

The process of determining work done by integrating power over time.

Perpendicular Vectors

Situation where force is at a 90-degree angle to velocity, resulting in zero power.

Parallel Vectors

Situation where force is in the same direction as velocity, maximizing power output.

Opposing Vectors

Situation where force opposes motion, indicating negative power and energy dissipation.

Horsepower (hp)

An imperial unit of power approximately equal to 746 Watts.

P = F·v

Formula relating power to force and velocity vectors.

P = dW/dt

Formula defining instantaneous power as the derivative of work with respect to time.

Work vs. Time Graph

Graph where the slope represents instantaneous power.

Power vs. Time Graph

Graph where the area under the curve represents total work done.

Lost Power

Power that is dissipated in non-ideal systems, often as heat due to friction.

Power and Efficiency Relation

Efficiency can be calculated as the ratio of output power to input power times 100%.