State and explain work energy principle.

Work-Energy Principle (Work-Energy Theorem)
The work-energy principle (also called the work-energy theorem) states that the work done by the net force on an object is equal to the change in its kinetic energy. In other words, when a force acts on an object and causes it to move, the work done by the force results in a change in the object's kinetic energy.
Mathematically, the work-energy principle can be expressed as:
W=ΔK=Kf−KiW = \Delta K = K_f - K_i
Where:
• WW is the work done by the force,
• ΔK\Delta K is the change in kinetic energy,
• KfK_f is the final kinetic energy,
• KiK_i is the initial kinetic energy.
Explanation:
1. Work Done by a Force:
o Work (WW) is the measure of energy transferred when a force is applied to an object, causing it to move. The work done by a constant force FF is calculated as:
W=F⋅d⋅cos⁡(θ)W = F \cdot d \cdot \cos(\theta)
Where:
o FF is the force applied,
o dd is the displacement of the object,
o θ\theta is the angle between the force and displacement vectors.
2. Change in Kinetic Energy:
o The kinetic energy (KK) of an object with mass mm and velocity vv is given by:
K=12mv2K = \frac{1}{2} m v^2
o The work-energy principle relates the work done on an object to the change in its kinetic energy. If a net force acts on an object and changes its velocity, the work done by that force is equal to the change in the object's kinetic energy.
3. Implications:
o If positive work is done on the object (force in the direction of motion), the object will gain kinetic energy.
o If negative work is done (force opposite to the direction of motion), the object will lose kinetic energy.
Example:
Consider a car of mass mm initially at rest. If a constant force FF acts on the car over a distance dd, the work done by the force is:
W=F⋅dW = F \cdot d
The car will accelerate and gain kinetic energy. If the car’s final speed is vfv_f, the change in kinetic energy is:
ΔK=12mvf2−0=12mvf2\Delta K = \frac{1}{2} m v_f^2 - 0 = \frac{1}{2} m v_f^2
According to the work-energy principle:
F⋅d=12mvf2F \cdot d = \frac{1}{2} m v_f^2
Thus, the work done on the car is directly responsible for the change in its kinetic energy.
Summary:
The work-energy principle states that the work done by the net force on an object is equal to the change in its kinetic energy. This principle is fundamental in mechanics and helps to explain how forces cause objects to accelerate or decelerate.