Unit 4 Overview: Energy

Unit 4: Energy – An Essential Foundation

Unit 4 introduces energy as an alternative method for solving problems explored in Units 1-3, providing a powerful toolset for tackling more advanced concepts in later units. Energy-related topics make up 16-24% of the AP Physics 1 exam and require 19-22 class periods to cover. Mastery of these foundational ideas is crucial for success in both the exam and understanding physics holistically.

Applicable Big Ideas

1. Big Idea #3: Force Interactions

   • How does pushing something give it energy?

2. Big Idea #4: Change

   • How is energy exchanged and transformed within or between systems?

3. Big Idea #5: Conservation

   • How does the law of conservation of energy govern interactions between objects and systems?

Key Concepts

• Systems
• Work 
  $W$
• Power
  $P$
• Gravitational Potential Energy
  $U_g$
• Elastic Potential Energy
  $U_{sp}$
• Kinetic Energy
  $K$
• Conservation of Energy

4.1 Open and Closed Systems: Energy

Open Systems

• Matter and energy can be exchanged with surroundings.
• Example: A pot of boiling water transfers heat from the stove while losing steam to the air.

Closed Systems

• Matter remains constant, but energy exchange is possible.
• Example: A sealed soda can transfers heat with its surroundings but retains its contents.

Conservation of Energy

• Open systems: Total energy of the system and surroundings remains constant.
• Closed systems: Total energy within the system remains constant, barring external transfers.

4.2 Work and Mechanical Energy

Work $W$

The transfer of energy through a force applied over a distance:

$$W=Fd\cos \theta$$

• 
  $F$

  : Force applied.

• 
  $d$

  : Displacement.

• 
  $\theta$

  : Angle between force and displacement.

Units: Joules (J)
Positive work increases energy; negative work decreases it.

Mechanical Energy

The sum of an object’s kinetic energy (KE) and potential energy (PE):

$$\text{Mechanical Energy} = KE + PE$$

Kinetic Energy $KE$

Energy of motion:

$$KE = \frac{1}{2}mv^2$$

• 
  $m$

  : Mass.

• 
  $v$

  : Velocity.

Potential Energy $PE$

Gravitational PE: Energy from height above a reference point:

$$PE_g = mgh$$

• 
  $m$

  : Mass.

• 
  $g$

  : Gravitational acceleration

  $9.8 \, \text{m/s}^2$

  on Earth.

• 
  $h$

  : Height.

Elastic PE: Energy stored in springs or elastic materials:

$$PE_{sp} = \frac{1}{2}kx^2$$

• 
  $k$

  : Spring constant.

• 
  $x$

  : Displacement from equilibrium.

Conservation of Mechanical Energy

$$KE_i + PE_i = KE_f + PE_f$$

​

In a closed system with no non-conservative forces (e.g., friction), total mechanical energy remains constant.

4.3 Conservation of Energy, the Work-Energy Principle, and Power

Work-Energy Principle

The work done on an object equals its change in kinetic energy:

$$W = \Delta K$$

Where:

$$\Delta K = KE_f – KE_i$$

​

Power $P$

Rate of work or energy transfer:

$$P = \frac{W}{t}$$

• 
  $W$

  : Work done.

• 
  $t$

  : Time.

Units: Watts (W), where

$1 \, \text{W} = 1 \, \text{J/s}$

Instantaneous Power:

$$P = Fv$$

Where:

• 
  $F$

  : Force applied.

• 
  $v$

  : Velocity.

Applications of Power

• In engines, the rate of combustion determines the car’s acceleration.
• In household appliances, power ratings indicate energy consumption.

Practical Examples

1. Roller Coasters:

   • Convert gravitational
     $PE$

      to

     $KE$

     for thrilling speeds on descents.

2. Hydroelectric Plants:

   • Transform water’s
     $PE_g$

     ​ into electrical energy via turbines.

3. Regenerative Braking:

   • Convert
     $KE$

      of a car into electrical energy for storage.

4. Solar Panels:

   • Turn sunlight’s electromagnetic energy into electricity.

Key Takeaways

1. Energy underpins physical interactions, from motion to heat transfer.
2. Conservation laws govern energy transformations and system behaviors.
3. Work and power quantify energy’s practical applications, such as in vehicles and power plants.