Question

derive work energy theorem.​

Answer 1

Solution:

Work:

• The scalar product of force & displacement is known as workdone.
• W = F.S
• W = F.S cos Ф

Energy:

• The ability or capacity to doing work is called energy.

Work - Energy Theorem:

⇒ w = ΔK.E

⇒ w = K - kᵢ     ........(1)

From 3rd Equation of motion,

⇒ v² = u² + 2as

⇒ v² - u² = 2as      ..........(2)

Now, multiply m/2 both the sides

$\sf{\implies \dfrac{mv^{2}}{2}-\dfrac{mv^{2}}{2}=\dfrac{m}{2}(2as)}$

⇒ (K.E)f - (K.E)ᵢ = F.S

⇒ W = (K.E)f - (K.E)ᵢ

⇒ W = ΔE

Hence Proved!!

Answer 2

Answer:

Work:

↔It is the dot product of Force and displacement (in vector form)

Work,W=F.S

W=Fscosθ

where θ is the angle between force and displacement

W=FS(in scalar form)

Energy:

The ability to do work is called Energy

Work energy theorem:

Statement:

Work energy theorem states that work done by conservative forces is the change in kinetic energy

It is represented as

$\sf work =\bigtriangleup K.E$

Proof:

according to laws of motion

$= > {v}^{2} - {u}^{2} = 2as$

$\underline{\sf multiplying \:with\: \dfrac{m}{2}\: on \:both \:sides}$

$= > \dfrac{m {v}^{2} }{2} - \dfrac{m {u}^{2} }{2} = \dfrac{m}{2} (2as) \\ \\ = > final \: k.e - initial \: k.e = ma(s)$

$\sf K.E_{final}-K.E_{initial}=W$

$\boxed{\sf work=\bigtriangleup K.E}$

Hence proved!!