Work, Energy, & Power - Formulas and Equations - College Physics
Work, Energy, and Power Explained
Understanding Work Done by a Force
- The work done on a block resting on a frictionless floor is calculated as the product of force and displacement.
- When pulling the block with tension at an angle θ to the displacement vector, work can be computed using W = F cdot D cdot cos(theta) .
- If the components of force and displacement are known but not the angle, use the dot product formula to find total work done in both x and y directions.
- Work is also defined as the change in kinetic energy (Work-Energy Theorem), expressed as W = Delta KE = 1/2 m (v_f^2 - v_i^2) .
Potential Energy and Conservative Forces
- The work done by conservative forces (e.g., gravity) equals the negative change in potential energy: W = -Delta PE . Gravitational potential energy can be represented as PE = mgh .
- For springs, elastic potential energy is given by PE_spring = 1/2 kx^2 , where k is spring constant and x is displacement from equilibrium.
- The work done against gravity or springs can be calculated using changes in height or position respectively.
Work Done by Gases
- When gases expand against a piston, they perform work calculated as W = -PDelta V , where P is pressure and ΔV is change in volume. This highlights another context for calculating work.
Defining Power
- Power quantifies how quickly work is done or energy transferred; it’s defined as P = W/t . Energy can exist in forms like kinetic or potential energy while work represents its transfer mechanism.
- Units of measurement include Joules for energy/work and Watts for power; 1 Watt equals 1 Joule per second. A 500-watt generator transfers 500 Joules every second.
Relationships Between Work, Power, and Velocity
- Power can also be expressed through velocity: P = Fv , linking force directly to motion over time. Instantaneous power relates to force applied at any moment during movement.
Understanding Power and Energy: Kilowatts vs. Kilowatt-Hours
Key Concepts of Power and Energy
- The relationship between force, velocity, and power is highlighted, emphasizing that kilowatts measure power while kilowatt-hours measure energy.
- It is clarified that a kilowatt-hour is not a unit of power but rather a unit of energy consumption.
- Electric bills typically reflect usage in kilowatt-hours, indicating the total energy consumed over a month.