Work
work is said to be done when a force causes displacement of an object.
W = F S cos θ
work is a scalar quantity.
SI unit is joule or Nm.
Work Done by a Variable Force
When the force acting on an object changes during motion, it is called a variable force. In this case, the simple formula W = F S cosθ cannot be used directly.
Work = ∫dw = ∫ F ds cosθ
work = area under the F vs S graph
Conservative and Non-Conservative
Forces
Conservative Forces
A force is called conservative if the work done by it depends only on the initial and final positions, not on the path followed.
●Total work done over a closed path is zero.
●A definite potential energy can be associated with the force.
●Total mechanical energy (KE + PE) remains constant.
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●Examples: Gravitational force, electrostatic force, spring force.
Non-Conservative Forces
A force is called non-conservative if the work done by it depends on the path followed between two points.
●Work done over a closed path is not zero.
●No unique potential energy function can be defined.
●Mechanical energy is not conserved (energy is dissipated).
●Examples: Frictional force, air resistance, viscous force.
Potential Energy
Potential energy is the energy possessed by a body due to its position or configuration.
●Potential energy is defined only for conservative forces (e.g., gravitational, electrostatic,spring).
General Differential Formula of Potential Energy
F = -dU/dx
Work Energy Theoram
The work done by all forces acting on an object is equal to the change in its kinetic energy.
W = (KE)f — (KE)i = ½mv² — ½mu²
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