Power (physics)

**Definition and Units of Power:**
– Power is the rate at which work is done over time.
– Mechanical power can be expressed as the product of force and velocity.
– Power is measured in watts (W) in the SI system.
– Additional units include horsepower (hp), ergs per second, foot-pounds per minute, dBm, calories per hour, BTU per hour, and tons of refrigeration.
– One mechanical horsepower is approximately equal to 745.7 watts.

**Average and Instantaneous Power:**
– Average power is the work done or energy converted per unit of time.
– Instantaneous power is the limiting value of average power as the time interval approaches zero.
– When power is constant, work done in a time period can be calculated as power multiplied by time.
– In energy conversion contexts, the symbol E is often used for power.
– Instantaneous power is the derivative of work with respect to time.

**Mechanical Power and Mechanical Advantage:**
– Power in mechanical systems is the combination of forces and movement.
– Mechanical power is the product of force on an object and the object’s velocity.
– Power in rotational systems is the product of torque and angular velocity.
– In fluid power systems, power is given by pressure multiplied by volumetric flow rate.
– Mechanical advantage is the ratio of output force to input force.
– These relationships define the maximum performance of a device based on velocity ratios.
– Mechanical advantage is crucial for determining device efficiency and gear ratios.

**Radiant Power and Related Concepts:**
– Power is related to intensity at a radius.
– The power emitted by a source can be written as: P(r) = I(4πr^2).
– Includes concepts like simple machines, orders of magnitude (power), pulsed power, and intensity in the radiative sense.
– Power gain is discussed for linear, two-port networks.

**Classical Mechanics Dimensions and Facts:**
– Burning coal produces around 15-30 megajoules per kilogram, while detonating TNT produces about 4.7 megajoules per kilogram.
– Classical mechanics SI units include linear/translational and angular/rotational quantities.
– Dimensions in classical mechanics include weighted position, moment of inertia, mass flow rate, momentum, impulse, angular momentum, and angular impulse.