4a._work_energy_power (1).pdf
Work, Energy, and Power Notes Summary
Overview
Energy Principle: Energy cannot be created or destroyed, only transformed.
Kinematics and Dynamics: Focused on understanding changes in motion.
Energy: An Overview
Definition: Exists in various forms (gravitational, kinetic, thermal, etc.) and is difficult to define.
Conservation of Energy: Energy in a closed system remains constant; it changes forms but is not lost.
Work
Definition: Involves exerting a force over a distance.
Formula: W = F · d (if F is parallel to d).
Units: Joules (J), where 1 J = 1 N · m.
Types of Work: Positive, negative, and zero work, depending on energy change and direction of force.
Work at an Angle
Formula: W = F · d · cos(θ).
Explanation: Only the component of force in the direction of displacement does work. Demonstrates how angle affects work calculation.
Examples:
Pushing a box with 10 N at 30° over 5 m yields approximately 43.3 J.
Applying 15 N at 60° over 4 m yields 30 J.
Kinetic Energy (KE)
Definition: Energy due to motion.
Formula: KE = 1/2 mv².
Work-Energy Theorem: Work done equals the change in kinetic energy.
Potential Energy (PE)
Definition: Energy stored due to position.
Gravitational Potential Energy Formula: PE = mgh.
Conservative Forces: Work done by these forces is path-independent.
Conservation of Mechanical Energy
Total Mechanical Energy: E = KE + PE.
Conservation Principle: In absence of nonconservative forces, initial total energy equals final total energy.
Power
Definition: Rate at which work is done.
Formula: P = W/t or P = F · v.
Units: Watts (W), where 1 W = 1 J/s.
Summary
Work: Energy change due to force, formulas W = Fd and W = ΔKE.
Energy Conservation: Total initial energy = total final energy in closed systems.
Power: Measures work rate, with formulas involving force and velocity.
Work, Energy, and Power Notes
Overview
Energy Principle: Energy cannot be created or destroyed, only transformed.
Kinematics and Dynamics: Focus on understanding changes in motion.
Energy: An Overview
Definition: Hard to define; exists in different forms (gravitational, kinetic, thermal, etc.).
Conservation of Energy: In a closed system, energy remains constant; it changes forms but is not lost.
Work
Definition: Work is done by exerting a force over a distance.
Formula: ( W = F \cdot d ) (if F is parallel to d).
Units: Measured in Joules (J), where 1 J = 1 N · m.
Types of Work:
Positive Work: Increases energy.
Negative Work: Decreases energy.
Zero Work: Occurs when force is applied perpendicular to displacement.
Work at an Angle
Formula: Work done by a force at an angle is calculated as: [ W = F \cdot d \cdot \cos(\theta) ] where:
W = work done (in Joules),
F = magnitude of the applied force (in Newtons),
d = distance over which the force is applied (in meters),
( \theta ) = angle between the force vector and the displacement vector.
Detailed Explanation: When a force acts at an angle, only the component of the force that aligns with the direction of displacement contributes to the work done. The cosine function is used to calculate this effective force component.
Examples:
When a person pushes a box with a force of 10 N at a 30-degree angle over a distance of 5 meters, the work done can be calculated as: [ W = 10 \cdot 5 \cdot \cos(30^{\circ}) \approx 43.3 \text{ J} ]
For a force of 15 N applied at a 60-degree angle while moving an object 4 meters, the work done would be: [ W = 15 \cdot 4 \cdot \cos(60^{\circ}) = 30 \text{ J} ] These scenarios demonstrate how to apply the formula when dealing with forces at angles.
Kinetic Energy (KE)
Definition: The energy an object possesses due to its motion.
Formula: ( KE = \frac{1}{2}mv^2 ).
Work-Energy Theorem: The work done on an object is equal to the change in its kinetic energy.
Potential Energy (PE)
Definition: Energy stored based on the position of an object.
Gravitational Potential Energy Formula: ( PE = mgh ).
Conservative Forces: The work done by these forces does not depend on the path taken.
Conservation of Mechanical Energy
Total Mechanical Energy: ( E = KE + PE ).
Conservation Principle: In the absence of nonconservative forces, the initial total energy equals the final total energy.
Power
Definition: The rate at which work is performed.
Formula: ( P = \frac{W}{t} ) or ( P = F \cdot v ).
Units: Measured in Watts (W), where 1 W = 1 J/s.
Summary
Work: The force causing a change in energy, with formulas ( W = Fd ) and ( W = \Delta KE ).
Energy Conservation: The total initial energy equals the total final energy in sealed systems.
Power: Indicates how quickly work is executed, with formulas relating force and velocity.
Examples
Work Calculation: Lifting a 2 kg book 3 meters results in 60 J of work.
Kinetic Energy: A 0.1 kg ball traveling at 30 m/s has 0.15 J of kinetic energy.
Potential Energy: A 2 kg ball at a height of 1.5 meters has 30 J of potential energy.
This summary captures the key concepts of work, energy, and power for study and exam preparation.