Glossary
Angle between force and velocity (θ)
The angle formed between the direction of the applied force and the direction of the object's motion, crucial for calculating the effective component of force for power.
Example:
If you push a lawnmower, the angle between force and velocity determines how much of your effort goes into moving it forward versus pushing it into the ground.
Average Power
The total energy transferred or work done divided by the total time interval over which the transfer or work occurred.
Example:
If you lift a box requiring 100 J of work over 5 seconds, your average power output is 20 W.
Average Power
Average power is the total energy transferred or work done divided by the total time taken for that transfer or work.
Example:
If a weightlifter lifts a 100 kg barbell 2 meters in 2 seconds, their average power output is (100 kg * 9.8 m/s² * 2 m) / 2 s = 980 W.
Change in Energy (ΔE)
The difference between the final and initial energy states of a system, representing the amount of energy transferred or converted.
Example:
When a ball falls, its gravitational potential energy undergoes a change in energy as it converts to kinetic energy.
Change in Time (Δt)
The duration over which an event or process occurs, used in calculating average rates.
Example:
Measuring the change in time it takes for a sprinter to run 100 meters helps determine their average speed and power output.
Derivative of Work with respect to time
A calculus-based definition of instantaneous power, found by taking the derivative of the work function with respect to time ($P = dW/dt$).
Example:
If the work done by a variable force is given by Joules, then the instantaneous power is found by taking the derivative of Work with respect to time, yielding Watts.
Dot product
A mathematical operation between two vectors that results in a scalar quantity, representing the product of their magnitudes and the cosine of the angle between them.
Example:
When calculating the power generated by a force, the dot product ensures that only the component of the force parallel to the velocity contributes to the power output.
Force
Force is a push or a pull that can cause an object to accelerate, change its momentum, or deform.
Example:
The gravitational force causes objects to fall towards the Earth.
Force component parallel to velocity (F||)
The portion of the applied force that acts in the same direction as the object's velocity, directly contributing to the work done and power delivered.
Example:
When pulling a sled, only the force component parallel to velocity (the horizontal pull) contributes to the power used to move it forward.
Force times Velocity
A formula for power calculated as the dot product of the force acting on an object and its instantaneous velocity ($P = \vec{F} \cdot \vec{v}$).
Example:
A rocket engine generating 1,000,000 N of thrust while moving at 2000 m/s produces 2 billion Watts of power using the Force times Velocity relationship.
Instantaneous Power
The power being delivered or consumed at a precise moment, calculated using the force and velocity at that instant.
Example:
As a rocket accelerates, its instantaneous power output continuously increases because both its engine thrust and velocity are changing.
Instantaneous Power
Instantaneous power is the rate at which work is done or energy is transferred at a specific moment in time.
Example:
The power meter on a bicycle shows the cyclist's instantaneous power output, which can fluctuate rapidly during a ride.
Joules per second (J/s)
An alternative unit for power, explicitly showing that power is the amount of energy transferred or work done divided by the time taken.
Example:
If a crane lifts a 500 kg load 10 meters in 5 seconds, its power output is 9800 Joules per second (or 9.8 kW).
Power
The rate at which energy is transferred, transformed, or work is done. It quantifies how quickly energy changes forms or moves within a system.
Example:
A powerful engine can accelerate a car from 0 to 60 mph in just a few seconds, demonstrating a high rate of energy conversion from chemical to kinetic.
Power
Power measures the rate at which energy is transferred or converted, indicating how quickly work is done.
Example:
A powerful sports car engine demonstrates high power output by accelerating rapidly.
Power
The rate at which work is done or energy is transferred, indicating how quickly an action is performed.
Example:
A high-performance sports car demonstrates immense power by accelerating rapidly, completing a large amount of work in a very short time.
Scalar Quantity
A scalar quantity is a physical quantity that has magnitude (a numerical value) but no associated direction.
Example:
Temperature, mass, and energy are examples of scalar quantities.
Scalar quantity
A physical quantity that is fully described by its magnitude (a numerical value) alone, without any direction.
Example:
Temperature, mass, and power are all scalar quantities; they don't have a direction associated with them.
Velocity
Velocity is the rate of change of an object's position, including both its speed and direction.
Example:
A satellite orbiting Earth at 7,000 m/s has a constant speed but its velocity is constantly changing due to its changing direction.
Velocity (v)
The rate of change of an object's position, including both its speed and direction.
Example:
A car traveling at a constant velocity of 60 mph east has a specific speed and direction.
Watt (W)
The SI unit of power, equivalent to one joule of energy transferred or converted per second.
Example:
A 100-watt lightbulb consumes 100 joules of electrical energy every second to produce light and heat.
Watts (W)
The standard SI unit for power, defined as one Joule of work done or energy transferred per second.
Example:
A typical household microwave oven might operate at 1000 Watts, meaning it uses 1000 Joules of energy every second.
Work
The energy transferred to or from an object by a force acting on it over a displacement. It is a scalar quantity.
Example:
Pushing a heavy box across the floor requires work to be done against friction, transferring energy to the box.
Work
Work is the energy transferred to or from an object by a force acting over a displacement.
Example:
Pushing a heavy box across a rough floor requires work to be done against the friction force.
Work vs. Time graph (slope)
On a graph where work is plotted on the y-axis and time on the x-axis, the slope of the line at any given point represents the instantaneous power.
Example:
If a Work vs. Time graph shows a curve that is getting steeper, it indicates that the instantaneous power (the slope) is increasing over time.
Work-Energy Theorem
The Work-Energy Theorem states that the net work done on an object is equal to the change in its kinetic energy.
Example:
If a car's engine does 50,000 J of net work on the car, the car's kinetic energy will increase by 50,000 J, as per the Work-Energy Theorem.