Formula Sheet: Work, Energy and Power

Yashwant Parihar,

In this post, we will learn Class 11 Chapter 5 Work, Energy and Power formulas with the help of the Formula Sheet. We have compiled a complete Work, Energy, and Power formula sheet, covering everything from the Work-Energy Theorem and Potential Energy to Collisions and Power.

Work, Energy and Power Formula Sheet

1. Work Done

Constant Force:

W=F.s=FsCosθW = F.s = FsCos\theta

Vairable Force:

W=∫x1x2F(x)dxW = \int_{x_1}^{x_2} F(x)dx

Where, W = Work, F = Force, s = Displacement

Work done by Gravity: W = ±mgh
Work done by a Spring:

W=12k(xi2−xf2)W = \frac{1}{2}k(x_i^2 – x_f^2)

2. Kinetic and Potential Energy

Kinetic Energy:

K=12mv2K=\frac{1}{2}mv^2

Relation Between K.E. and Momentum(p):

K=p22mK = \frac{p^2}{2m}

Potential Energy:

U=mghU = mgh

Elastic Potential Energy:

U=12kx2U = \frac{1}{2}kx^2

3. Work-Energy Theorem

Work Done by all Forces:

Δk=Kf−Ki\Delta{k} = K_f – K_i

4. Conservative vs. Non-Conservative Forces

Conservatives Forces: Work depends only on initial and final positions (e.g. Gravity, Elctrostatic).

F=−dUdxF = -\frac{dU}{dx}

Non Conservative Forces: Work depends on the path taken (e.g. Friction, Viscous Force).

5. Power

Average Power:

Pavg=ΔWΔtP_{avg} = \frac{\Delta{W}}{\Delta{t}}

Instantaneous Power:

P=dWdt=F.vP = \frac{dW}{dt} = F.v

1 HorsePower = 746 Watts.

6. Collisions (1D and 2D)

Law of Conservation of Momentum:

m1u1+m2u2=m1v1+m2v2m_1u_1 +m_2u_2 = m_1v_1 + m_2v_2

Coefficent of Restitution:

e=RelativeVelocityofSeprationRelativeVelocityofApproach=v2v1e = \frac {Relative\:Velocity\:of\:Sepration}{Relative\:Velocity\:of\:Approach} = \frac{v_2}{v_1}

Elastic Collision: e = 1
Inelastic Collision: 0 < e < 1
Perfect Inelastic: e = 0

Final Velocities in 1D Elastic Collision:

v1=(m1−m2m1+m2)u1+(2m2m1+m2)u2v_1 = \left (\frac{m_1-m_2}{m_1+m_2} \right)u_1 + \left ( \frac{2m_2}{m_1 +m_2} \right)u_2

7. Vertical Circular Motion (The “Secret” Trick)

For an obejct to complete a vericle cycle of radius R:

Minimum velocity at Bottom:

vmin=5gRv_{min} = \sqrt{5gR}

Minimum velocity at top:

vtop=3gRv_{top} = \sqrt{3gR}
Formula Sheet Physics Formula Sheet

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