Energy of motion (kinetic energy) Knowledge-Based Study

Study notes

1. Kinetic energy is the energy possessed by an object due to its motion. Any object that has mass and is moving with a certain speed has kinetic energy. If an object is at rest, its kinetic energy is zero.

   Like all forms of energy, kinetic energy is a scalar quantity, meaning it has magnitude but no directional component. In the International System of Units (SI), kinetic energy is measured in joules (J), where one joule equals one kilogram meter squared per second squared (1 J = 1 kg·m²/s²).

   Translational kinetic energy $E_k$ depends directly on the mass of the object and the square of its speed:

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

   • m is the mass of the object in kilograms (kg).
   • v is the magnitude of the velocity (speed) in meters per second (m/s).

   Because speed is squared in this relationship:

   • Doubling the mass of an object while keeping its speed constant doubles its kinetic energy.
   • Doubling the speed of an object while keeping its mass constant quadruples ($2^2 = 4$) its kinetic energy.

   The connection between forces, displacement, and kinetic energy is established through the Work-Energy Theorem. When a net external force acts on an object over a displacement, it performs net work $W_{\text{net}}$.

   The theorem states that the net work done on a rigid object equals the change in its kinetic energy:

   $$W_{\text{net}} = \Delta E_k = E_{k,\text{final}} - E_{k,\text{initial}}$$

   If the net work done is positive, the object speeds up and its kinetic energy increases. If the net work done is negative (such as work done by friction opposing motion), the object slows down and its kinetic energy decreases.

   Understanding kinetic energy requires keeping several fundamental principles in mind:

   • Kinetic energy can never be negative: Since mass is positive and speed is squared ($v^2 \ge 0$), kinetic energy is always zero or positive.
   • Independence of direction: Two identical vehicles moving at the same speed in opposite directions have different velocities, but identical kinetic energies.
   • Frame of reference: Because velocity depends on the chosen frame of reference, kinetic energy is also relative to the observer's frame of reference.