05Class 11 Physics

Work, Energy and Power formulas

Work, energy, power and collision formulas. Reach for energy first when a problem cares about speeds and positions and not about time.

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Work and energy

Work by a constant force: $\displaystyle W = \vec F\cdot\vec d = Fd\cos\theta$
Work by a variable force: $\displaystyle W = \int_{x_i}^{x_f} F\,dx$
Kinetic energy: $\displaystyle K = \tfrac12 mv^2 = \frac{p^2}{2m}$
Work-energy theorem: $\displaystyle W_{\text{net}} = \Delta K$
Gravitational potential energy: $\displaystyle U = mgh$
Near Earth's surface.
Spring potential energy: $\displaystyle U = \tfrac12 kx^2$
Spring force: $\displaystyle F = -kx$

Coefficient of restitution: $\displaystyle e = \frac{v_2 - v_1}{u_1 - u_2}$
e = 1 is elastic, and e = 0 is perfectly inelastic.
1D elastic collision: $\displaystyle v_1 = \frac{(m_1 - m_2)u_1 + 2m_2u_2}{m_1 + m_2}$
Swap the subscripts to get v₂.
Perfectly inelastic collision: $\displaystyle v = \frac{m_1u_1 + m_2u_2}{m_1 + m_2}$

Assuming kinetic energy is conserved in every collision. Momentum is conserved, and kinetic energy only in elastic collisions.
Using Fd when force and displacement aren't parallel. You need the cos θ.
Using mgh for large heights. Far from Earth's surface, use the gravitational form from the next chapters.

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