Скачать или смотреть Work, Energy & Power || JEE Main| Advanced || NEET

Work, Energy & Power || JEE Main| Advanced || NEET
Let’s consider about the this rectilinear motion equation.
𝑣^2 − 𝑢^2=2𝑎𝑠
Here, 𝑣=𝐹𝑖𝑛𝑎𝑙 𝑠𝑝𝑒𝑒𝑑, 𝑢=𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑠𝑝𝑒𝑒𝑑, 𝑠=𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒𝑑
𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑖𝑛𝑔 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠 𝑏𝑦 𝑚/2
〖𝑚𝑣〗^2/2− 〖𝑚𝑢〗^2/2= 𝑚/2 2𝑎𝑠
〖𝑚𝑣〗^2/2− 〖𝑚𝑢〗^2/2= 𝑚/2 2𝑎𝑠
1/2 𝑚𝑣^2 − 1/2 𝑚𝑢^2=𝑚𝑎𝑠=𝐹.𝑠
This step follows from Newton’s Second Law.
We can generalise this equation to three dimensions by employing vectors.
𝑣^2 − 𝑢^2=2𝑎.𝑑
Once again multiplying both sides by 𝑚/2
1/2 𝑚𝑣^2 − 1/2 𝑚𝑢^2=𝑚𝑎𝑑=𝐹.𝑑
This equation provides a motivation for the definition of work and kinetic energy.
The left side of the equation is difference in the quantity ‘half the mass times the
square of the speed’ from its initial value to its final value.
We call each of these quantities the ‘kinetic energy’, denoted by K.
The right side is a product of the displacement and the component of the
force along the displacement.
This quantity is called ‘work’ and is denoted by W.
Then,
𝐾_𝑓 − 𝐾_𝑖=𝑊
𝐾_𝑓 − 𝐾_𝑖=𝑊
where Ki and 𝐾_𝑓 are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts.
Work is done by a force on the body over a certain displacement. Equation is also a special case of the work-energy (WE) theorem :
The change in kinetic energy of a particle is equal to the work done on it by the net force.
We shall generalise the above derivation to a varying force in a later section.
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