The ###-energy_theorem_0### connects the work done on a to its change in . It's a powerful tool for analyzing motion, allowing us to calculate velocities and displacements without needing to know the entire path of an object.
This theorem bridges the concepts of , work, and energy. By understanding how work relates to changes in kinetic energy, we can solve complex problems involving particle motion and in various physical scenarios.
Work-Energy Theorem
Work-energy theorem for particle motion
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States done on a particle equals change in its kinetic energy Wnet=ΔKE
Wnet represents done on particle by all forces
ΔKE represents change in particle's kinetic energy
Calculate net work by summing work done by each force acting on particle Wnet=W1+W2+...+Wn
Calculate work done by a force using product of force and in direction of force W=F⋅d
For constant force W=Fdcosθ, θ represents angle between force and vectors
For force varying with position W=∫x1x2F(x)dx
Calculate change in kinetic energy by subtracting initial from final kinetic energy ΔKE=KEf−KEi=21mvf2−21mvi2
m represents particle's
vi and vf represent particle's initial and final velocities
Determine particle's final or displacement by applying given initial conditions and acting forces (sliding block, )
Work-energy theorem relates to energy transfer between different forms (e.g., kinetic to )
Forces from motion using work-energy
Determine net work done on particle using work-energy theorem if initial and final velocities (or kinetic energies) and displacement are known
Rearrange work-energy theorem to solve for net work Wnet=ΔKE=21mvf2−21mvi2
Calculate work done by unknown force using net work and known forces Wunknown=Wnet−(W1+W2+...+Wn)
Determine average force exerted on particle using work-displacement relationship Favg=dcosθWunknown once work done by unknown force is calculated (pulling a , pushing a )
Kinetic energy changes from net work
Calculate change in particle's kinetic energy directly from net work done on it ΔKE=Wnet
To find change in kinetic energy:
Calculate net work done by all forces acting on particle
Equate net work to change in kinetic energy
Alternatively, calculate change in kinetic energy using particle's initial and final velocities ΔKE=21mvf2−21mvi2
Equation derived from work-energy theorem and definition of kinetic energy KE=21mv2
Understanding relationship between work and changes in kinetic energy is crucial for analyzing motion of particles under influence of forces (, )
Energy Conservation and Mechanical Energy
principle states that total energy in an isolated system remains constant
is the sum of kinetic and potential energy in a system
In conservative systems, is conserved when no non-conservative forces do work
Power is the rate at which work is done or energy is transferred, measured in watts (W)