AP Physics C Mechanics: Work, Energy, and Power Lecture Notes

Introduction

• Topics Covered:
  • Work
  • Energy
  • Power
• Focus on AP Physics C Mechanics curriculum

Work

Work by a Constant Force

• Equation: Work done by a constant force = dot product of force and displacement.
  • Can also be expressed as: Force x Displacement x Cos(theta)
• Dot Product: Multiplies component of force in the direction of displacement.
• Example:
  • Force: 2.7i - 3.1j Newtons
  • Displacement: 4.6i meters
  • Work: 12.42 Joules using the dot product.
  • Work units: Joules (J)

Joules

• A joule is defined as a Newton meter.
• Newton defined as a kilogram meter per second squared.

Work by a Non-constant Force

• Equation: Integral from initial to final position of force with respect to position.
• Integral: Represents the area under the curve between the curve and the horizontal axis.

Hooke's Law & Springs

• Equation: Force of a spring = -kx
• Terms:
  • K: Spring constant (Newtons/meter)
  • x: Displacement from equilibrium
• Work by a Spring:
  • Uses integral formula due to variable force.
  • Result: Negative of the change in elastic potential energy.

Energy

Kinetic Energy

• Equation: KE = 1/2 x Mass x Velocity^2
• AP equation sheet uses K.

Gravitational Potential Energy

• Equation: U = Mass x Gravity x Height
• Symbol: U
• Important to identify horizontal zero line.

Energy Conservation Principles

• Energy cannot be created or destroyed.
• Non-isolated System: Change in energy = Sum of energy transferred in/out.
• Isolated System: Change in energy = 0
  • Change in mechanical + internal energy = 0

Work by Non-Conservative Forces

• Depends on path taken.
• Equation: Work = Change in mechanical energy
• Friction is a common non-conservative force.

Power

Definition

• Power is the rate at which work is done.
• Average Power: Work / Change in time
• Instantaneous Power: Derivative of work with respect to time.
• SI Unit: Watts (W)
  • 1 horsepower = 746 watts

Power Equations

• Equation: Power = Derivative of energy with respect to time.
• Graphical Interpretation: Area under power-time curve = Change in work.

Equilibrium

Types of Equilibrium

1. Neutral Equilibrium: Constant potential energy
2. Stable Equilibrium: Potential energy increases with displacement from equilibrium.
3. Unstable Equilibrium: Potential energy decreases with displacement.

Conclusion

• Reviewed work, energy, and power concepts.
• Emphasized understanding of equations and principles for AP Physics C.
• Next review available on integrals in kinematics.
• Encouragement to explore additional resources provided.