Study Notes: Energy, Work, and Power (Physics Ch. 7)

Energy, Work, and Power

Energy

Energy is defined as the ability to do work. It can be considered both as a process and as a property of a system or object.

• Ability to do work: Energy enables objects or systems to perform work.

• Process vs. Thing: Energy can be transferred or transformed but is not a tangible substance.

Work

Work is the transfer of energy that occurs when a force acts upon an object to cause displacement.

• Formula: $W = F d \cos \theta$ where F is the force, d is the displacement, and \theta is the angle between the force and displacement vectors.

• Units: Joules (J), where $1\,J = 1\,kg\,m^2/s^2$

• Work can be positive (force and displacement in the same direction) or negative (force and displacement in opposite directions).

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy.

• Equation: $W_{net} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$

• Kinetic Energy (KE): $KE = \frac{1}{2}mv^2$ where m is mass and v is speed.

• Kinetic energy is proportional to the square of the speed ($KE \propto v^2$).

Types of Energy

There are two main types of mechanical energy: kinetic and potential energy.

• Kinetic Energy: Energy of motion.

• Potential Energy: Stored energy due to position or configuration. For gravitational potential energy:

  • Equation: $PE = mgh$

  • Depends on mass (m), gravitational acceleration (g), and height (h).

  • Potential energy is a property of the system (object and Earth).

  • Position is key for potential energy.

Power

Power is the rate at which work is done or energy is transferred.

• Formula: $P = \frac{E}{t}$ where E is energy (or work) and t is time.

• Units: Watts (W), where $1\,W = 1\,J/s$

• Conversion factor: $1$ horsepower (hp) $= 746$ W

Conservation of Mechanical Energy

The conservation of mechanical energy principle states that the total mechanical energy (kinetic + potential) in a system remains constant if only conservative forces (like gravity) are acting.

• Equation: $E_i = E_f$ or $KE_i + PE_i = KE_f + PE_f$

• Mechanical energy is the sum of kinetic and potential energy.