Work in physics is done when a force causes displacement. The formula for work is W equals F times d times cosine theta, where F is the applied force in Newtons, d is the displacement in meters, and theta is the angle between the force and displacement vectors. The unit of work is Joules.
Power in physics is the rate at which work is done or energy is transferred. The basic formula for power is P equals W divided by t, where W is work done in Joules and t is time taken in seconds. Power can also be calculated as P equals F times v, where F is force and v is velocity. The unit of power is Watts.
Capability in physics refers to the ability or potential to do work or exert power. Unlike work and power, capability is not a formal physics quantity with specific units. Instead, it describes the maximum performance limits of systems. For example, engine capability refers to maximum power output, while battery capability refers to energy storage capacity. Capability is related to both work and power through performance limits.
The relationship between work and power is fundamental in physics. Power is defined as the rate of doing work, expressed as P equals W divided by t. This can be rearranged to show that work equals power times time. Higher power means the same amount of work can be done in less time, while the same power over more time results in more work being done. For example, a one hundred watt motor running for ten seconds does one thousand joules of work.
To summarize what we have learned: Work is force times displacement measured in Joules. Power is the rate of doing work measured in Watts. Capability refers to the potential to do work or exert power. The relationship between work and power is given by P equals W divided by t. These fundamental concepts are essential in physics and engineering applications.