BackWork and Kinetic Energy – Chapter 7 Study Notes
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Work and Kinetic Energy
Introduction
This chapter explores the concepts of work, kinetic energy, and power in classical mechanics. These ideas are fundamental for understanding how forces cause changes in motion and energy in physical systems.
Work Done by a Constant Force
Definition of Work
Work is done when a force causes a displacement of an object. If the force is constant and acts parallel to the displacement, the work done is given by:
Formula:
Units: The SI unit of work is the joule (J), where .
Direction: Only the component of force in the direction of displacement does work.
Work at an Angle
If the force is applied at an angle to the direction of displacement, only the component contributes to the work:
Dot Product: Work can be expressed as the dot product of force and displacement vectors: .
Sign of Work
Positive Work: (force and displacement in the same general direction)
Zero Work: (force perpendicular to displacement)
Negative Work: (force opposes displacement)
Work by Multiple Forces
When more than one force acts on an object, calculate the work done by each force and by the net force:
Example: Pushing a Gurney
An intern pushes an 87-kg patient on an 18-kg gurney, producing an acceleration of over .
To find the work done, use where is the net force required to accelerate the combined mass.
Kinetic Energy and the Work-Energy Theorem
Kinetic Energy
Kinetic energy is the energy of motion. For an object of mass moving at speed :
Units: Joules (J)
Work-Energy Theorem
The work-energy theorem states that the total work done on an object is equal to its change in kinetic energy:
Positive work increases kinetic energy (object speeds up).
Negative work decreases kinetic energy (object slows down).
Example: Airplane Takeoff
An airplane of mass has a kinetic energy of during takeoff. To find its speed, use and solve for .
Work Done by a Variable Force
Graphical Interpretation
When the force varies with position, the work done is the area under the force vs. position graph.
If the force changes in steps, sum the areas of rectangles under each segment.
For a continuously varying force, approximate with many small steps or use calculus.
Work Done by a Spring
The force required to stretch or compress a spring by a distance is given by Hooke's Law:
The work done in stretching or compressing the spring from to is:
k is the spring constant (N/m).
Power
Definition of Power
Power is the rate at which work is done or energy is transferred:
Units: Watt (W), where
Horsepower:
Power for Constant Speed
If an object moves at constant speed under a constant force in the direction of motion:
Summary Table: Key Formulas and Concepts
Concept | Formula | Units |
|---|---|---|
Work (constant force, parallel) | Joule (J) | |
Work (force at angle) | Joule (J) | |
Kinetic Energy | Joule (J) | |
Work-Energy Theorem | Joule (J) | |
Work by a Spring | Joule (J) | |
Power | Watt (W) | |
Power (constant speed) | Watt (W) |
Additional Info
These concepts are foundational for later topics in physics, including potential energy, conservation of energy, and mechanical systems.
Understanding the sign and direction of work is crucial for solving real-world problems involving forces and motion.
