(802) (New) AP Physics 1 - Unit 3 Review - Work, Energy, and Power - Exam Prep

Unit 3: Work, Energy, and Power - AP Physics 1

Kinetic Energy

• Definition: Kinetic energy is the energy of motion.

• Equation:

  • Kinetic Energy (KE) = 1/2 * m * v²

  • Where:

    • m = mass of the object

    • v = speed of the object (often represented as letter v in equations).

• Properties:

  • Kinetic energy cannot be negative.

  • Measurement is frame-dependent; for example, a car can have different kinetic energy based on the observer's frame of reference.

Work

• Definition: Work is the amount of mechanical energy transferred into or out of a system.

• Equation:

  • Work (W) = F * d * cos(theta)

    • Where:

      • F = force doing work on the system

      • d = displacement

      • theta = angle between force direction and displacement direction.

• Conservative vs. Nonconservative Forces:

  • Conservative Force: Work is independent of path; depends only on the initial and final states.

  • Nonconservative Force: Work depends on the path taken (e.g., friction, air resistance).

Mechanical Energy

• Types of Mechanical Energy:

  • Kinetic Energy

  • Gravitational Potential Energy

  • Elastic Potential Energy

Gravitational Potential Energy

• Equation:

  • Gravitational Potential Energy (PE) = m * g * h

    • Where:

      • m = mass

      • g = gravitational field strength

      • h = height above a reference point.

• Change in Gravitational Potential Energy:

  • Change in PE = m * g * (h_final - h_initial)

  • The height can be negative if the object is below the reference height.

• System Requirements: Potential energy requires two masses (e.g., an object and the Earth).

• General Form:

  • Gravitational PE = -G * (m1 * m2) / r, where G = gravitational constant, r = distance between mass centers.

  • Gravitational potential energy is negative when calculating between two masses.

Elastic Potential Energy

• Definition: Energy stored in elastic materials (e.g., springs, rubber bands).

• Equation:

  • Elastic Potential Energy (PE_e) = 1/2 * k * (delta x)²

    • Where:

      • k = spring constant

      • delta x = displacement from equilibrium position.

  • Can’t be negative due to squaring displacement.

Total Mechanical Energy

• Equation: E_initial = E_final (conservation of mechanical energy when net work is zero)

  • Equivalent to saying the total mechanical energy remains constant if only conservative forces are acting.

• For a single object system, mechanical energy is only kinetic.

• Changes in energy types must balance out through transfers into or out of the system.

Work-Energy Principle

• Definition: Net Work = Change in Kinetic Energy

  • Applies to systems experiencing both conservative and nonconservative forces.

• Example: A sliding book losing kinetic energy due to friction (work done on the system).

Power

• Definition: Power is the rate at which energy changes or is transferred.

• Equation:

  • Average Power = Change in Energy / Change in Time

  • Average Power = Work Done / Change in Time

  • Instantaneous Power = F * v * cos(theta)

    • Where:

      • F = force doing work

      • v = instantaneous velocity.

• Units:

  • Common unit for power is watts (W), where 1 W = 1 J/s.

  • J (joule) = N * m = kg * m²/s², thus W = kg * m²/s³.