Work-Energy for Rigid Bodies A rigid body is an object with a fixed shape and no deformation. We can define the work-energy of a rigid body in terms of the e...
A rigid body is an object with a fixed shape and no deformation. We can define the work-energy of a rigid body in terms of the energy it possesses when it performs a mechanical work on another object.
Mechanical work is the amount of energy transferred to an object when a force is applied to it. We denote the work done by a force with the symbol (W), and it is a scalar quantity, meaning it has only magnitude and no direction.
The work-energy theorem establishes a fundamental connection between mechanical work and the energy of the body. It states that the net work done on a body is equal to the change in its mechanical energy. Mathematically:
Where:
(W) is the work done in joules
(\triangle E_k) is the change in the body's kinetic energy in joules
Kinetic energy is a scalar quantity that represents the energy of motion and is directly proportional to the square of the object's velocity. Mathematically:
Where:
(m) is the mass of the body in kilograms
(v) is the velocity of the body in meters per second
Therefore, the work-energy theorem can be written as:
Examples:
When a force pushes a block across a frictionless surface, the work done by the force is equal to the increase in the block's kinetic energy.
When a ball is thrown in the air, the work done by the gravitational force is equal to the change in the ball's potential energy.
When a car brakes, the work done by the friction forces is equal to the decrease in the car's kinetic energy.
The work-energy theorem provides a powerful tool for understanding the dynamics of rigid bodies and analyzing the relationships between force, work, and energy