1.State Newton's Second Law of Motion.
Sol: The rate of change of momentum of a body is directly proportional to applied force: $\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a}$.
2.Define impulse and state its SI unit.
Sol: Impulse = Force $\times$ time duration = Change in momentum. Unit: $\text{N}\cdot\text{s}$ or $\text{kg}\cdot\text{m/s}$.
3.What is limiting friction?
Sol: The maximum value of static friction just before a body begins to slide.
4.State the condition for banking angle of a road without friction.
Sol: $\tan \theta = \frac{v^2}{rg}$.
5.A force of $20 \text{ N}$ acts on a mass of $5 \text{ kg}$ for $4 \text{ s}$. Find acceleration and final velocity from rest.
Sol: $a = \frac{F}{m} = \frac{20}{5} = 4 \text{ m/s}^2$. $v = u + at = 0 + 4(4) = 16 \text{ m/s}$.
6.A block of mass $10 \text{ kg}$ rests on a rough horizontal surface with coefficient of friction $\mu = 0.3$. Find force required to just move it.
Sol: Limiting friction $f_s = \mu N = \mu m g = 0.3 \times 10 \times 9.8 = 29.4 \text{ N}$.
7.An elevator of mass $1000 \text{ kg}$ ascends with acceleration $2 \text{ m/s}^2$. Find tension in cable ($g=10$).
Sol: $T - mg = ma \implies T = m(g+a) = 1000(10+2) = 12000 \text{ N}$.
8.A ball of mass $0.2 \text{ kg}$ moving at $20 \text{ m/s}$ is caught in $0.1 \text{ s}$. Find average stopping force.
Sol: $F = \frac{\Delta p}{\Delta t} = \frac{m(v-u)}{t} = \frac{0.2(0-20)}{0.1} = -40 \text{ N}$ (Retarding force = $40 \text{ N}$).
