Work, Energy and Power

• If Work done or energy are negative then the force is attractive.
• Work is done when a force displaces an object through a certain distance.
• Work done = F • S = F s cosθ.
• 1 Joule =1 Newton • 1 meter
• The SI unit of work done is joules and CGS is erg.
• Power is the rate of doing work, represented as P = W/t = Joule/sec = Watt.
• Work done is scalar whereas force and displacement are vector quantities therefore we use dot product to calculate work done.
• Power is also the rate of consumption of energy, represented as P = E/t = Joule/sec = Watt.
• Work done by a variable force is represented as dW = F • dx.
• If force is variable then calculus is used to calculate work done.
• Work done can be positive, zero, or negative.
• Force → displacement → work done → energy
• Mechanical Energy (M.E.) = Kinetic Energy (K.E.) + Potential Energy (P.E.).
• Energy is also measured in Joules and erg, In SI and CGS systems respectively.
• The Work Energy Theorem states that work done by a force is always equal to change in its Kinetic Energy.
• Work done by the gravitational force is called Gravitational Potential Energy.
• Work Done = ΔK.E.
• W = 1/2 mv²-1/2mu²
• W = F•s cos θ
• cos 0°*= 1
• W = F•s
• W = m•a•s
• v²-u² = 2as
• W = ΔK.E.
• W = 1/2 m•(v²-u²) is the Work Energy Theorem
• Mathematically, Hooke’s law is expressed as: F ∝ x (displacement from mean position) or F = -kx.
• If mass and velocity are given to us in a question, we can derive 2 quantities from this information: linear momentum (p=mv) and kinetic energy (K.E = 1/2mv²).
• W = m• |v²/2| is the kinetic energy of a freely falling body.
• W = K.E.(f) - K.E(i) is the kinetic energy of a freely falling body.
• dW = ma•dx is the differential of work done by an acceleration.
• DW = F•dx is the differential of work done by a force.
• In the equation, F = - KX, F is the force, x is the extension in length, and k is the spring constant (N/m)
• Elastic potential energy in spring is a variable force (because it’s a restoring force).
• a = dv/dt is the differential of acceleration.
• Hooke’s law states that the strain of the material is proportional to the applied stress within the elastic limit of that material.
• B is at a height H-x (x is the already travelled distance) where K.E.= 1/2 mv².
• W = 1/2mv² - 1/2mu² is the Work Energy Theorem
• T.E = K.E + P.E.
• C is just before touching the ground (almost at H=0) where K.E.= 1/2mv².
• p = √2m•K.E or K.E = p²/2m is the relation between kinetic energy of a freely falling body.