(455) Work, energy and power [IB Physics SL/HL]

Work

• Definition: Work is defined as the product of force and displacement, modified by the cosine of the angle between them.

• Equation: [ W = F imes S imes \cos(\Theta) ]

  • Variables:

    • ( W ): Work (Joules)

    • ( F ): Force applied (Newtons)

    • ( S ): Displacement (meters)

    • ( \Theta ): Angle between force and displacement

• Characteristics:

  • Work is a scalar quantity (no direction involved).

  • When force and displacement are in the same direction (( \Theta = 0 )), work is maximized.

  • No work is done when displacement is perpendicular to the force (( \Theta = 90^{\circ} )).

Work-Energy Theorem

• Concept: Work is a form of energy, measured in Joules, demonstrating that energy is conserved during work and movement.

Kinetic Energy

• Definition: Energy associated with moving objects.

• Equation: [ E_k = \frac{1}{2} mv^2 ]

  • Variables:

    • ( E_k ): Kinetic Energy

    • ( m ): Mass (kg)

    • ( v ): Velocity (m/s)

Potential Energy

• Gravitational Potential Energy: Energy stored due to an object's position in a gravitational field.

• Equation: [ E_p = mgh ]

  • Variables:

    • ( E_p ): Potential Energy

    • ( m ): Mass (kg)

    • ( g ): Acceleration due to gravity (9.81 m/s²)

    • ( h ): Height (meters)

• Spring Potential Energy: Energy stored in a compressed or stretched spring.

• Equation: [ E_p = \frac{1}{2} K \Delta x^2 ]

  • Variables:

    • ( K ): Spring constant (N/m)

    • ( \Delta x ): Displacement from equilibrium (meters)

Total Energy

• Definition: Total energy is the sum of kinetic and potential energy.

• Concept: Total energy is conserved in an isolated system, enabling energy calculations at different points in motion.

Power

• Definition: Power measures the rate at which work is done or energy is transferred.

• Main Equation: [ P = F \times V ]

  • Variables:

    • ( P ): Power (Watts)

    • ( F ): Force (Newtons)

    • ( V ): Velocity (m/s)

• Alternate Equation: [ P = \frac{E}{t} ]

  • Variables:

    • ( E ): Energy (Joules)

    • ( t ): Time (seconds)

• Units: Power is measured in Watts (Joules/second).

• Application: The power formula is useful across various physics topics, including mechanics and electricity.