1.State the Work-Energy Theorem.
Sol: Work done by net force equals change in kinetic energy: $W_{net} = \Delta K = K_f - K_i$.
2.Define conservative and non-conservative forces with examples.
Sol: Conservative force: Work done is independent of path (e.g. Gravity, Electrostatic). Non-conservative: Work depends on path (e.g. Friction, Viscosity).
3.State the potential energy formula of a compressed spring.
Sol: $U = \frac{1}{2} k x^2$.
4.What is coefficient of restitution ($e$) in a collision?
Sol: $e = \frac{\text{Relative velocity of separation}}{\text{Relative velocity of approach}} = \frac{v_2 - v_1}{u_1 - u_2}$.
5.A force $F = (3x^2 + 2x) \text{ N}$ acts on a body. Calculate work done in moving it from $x=0$ to $x=2\text{ m}$.
Sol: $W = \int_0^2 (3x^2 + 2x) dx = \left[ x^3 + x^2 \right]_0^2 = 8 + 4 = 12 \text{ Joules}$.
6.A bullet of mass $20 \text{ g}$ moving at $500 \text{ m/s}$ penetrates a sand bag and stops in $10 \text{ cm}$. Find kinetic energy lost and average retarding force.
Sol: $K = \frac{1}{2}(0.02)(500^2) = 2500 \text{ J}$. $F = \frac{K}{s} = \frac{2500}{0.1} = 25000 \text{ N} = 25 \text{ kN}$.
7.A pump lifts $1000 \text{ kg}$ of water to height $20 \text{ m}$ in $20 \text{ s}$. Find power of pump in kW ($g=10$).
Sol: $P = \frac{mgh}{t} = \frac{1000 \times 10 \times 20}{20} = 10000 \text{ W} = 10 \text{ kW}$.
8.A mass $m$ moving with speed $v$ collides head-on elastically with an equal mass at rest. Find final velocities.
Sol: In 1D elastic collision of equal masses, velocities interchange: First body stops ($v_1 = 0$), second body moves with initial speed of first ($v_2 = v$).
