Kinetic Energy and Work

Energy is conserved in a closed system. Energy is associated with a system of objects, and the energy values change when a force is applied to an object, causing it to move over a distance.

Work Done: When force is applied to an object to move a mass over a distance:

\[W = F \cdot d \cdot \cos(\theta)\]

where \(( \theta \)\) is the angle between the directions of displacement and the force.

Kinetic Energy: Kinetic energy is associated with the state of motion of an object:

\[K.E = \frac{1}{2} m v^2\]

Understanding an object’s kinetic energy provides key insights into the forces required to bring it to rest. For example, knowing the kinetic energy helps determine the opposing force needed for deceleration. This concept is also crucial in analyzing collision impacts, as it explains how energy influences the interaction between colliding objects.

Work-Energy Theorem

The change in kinetic energy of a particle is the net work done on the particle.

Power

Work quantifies the force and displacement properties. Power helps to understand the rate at which work is done.

Average Power:

\[P_{avg} = \frac{W}{\Delta t}\]

Instantaneous Power:

\[P = \frac{dW}{dt}\]

The instantaneous power can be expressed in terms of the force and velocity of an object:

\[P = F \cdot v \cdot \cos(\theta)\]