Q.A car of mass M moves upward with a constant speed v along an inclined road making an angle θ with the horizontal. If μ be the coefficient of friction between the road and the wheel of the car, show that the power of the engine of the car is P = vMg (sin θ + μ cos θ). OR A balloon at rest on the ground is rising upward with acceleration g/8. A stone is dropped from the balloon when it is at height H. Show that the time taken by the stone to touch the ground is 2√(H/g).

Friction is of three types - static, kinetic, and rolling - and each obeys the law f = mu*N (friction proportional to normal reaction, independent of contact area).

Types of friction:

1. Static friction - the opposing force that acts between two surfaces at rest relative to each other, preventing relative motion from starting; it adjusts itself (up to a maximum limiting value) to exactly balance the applied force.
2. Kinetic (sliding) friction - the opposing force that acts when one surface is actually sliding over another; it is roughly constant and generally slightly less than the maximum static friction.
3. Rolling friction - the (much smaller) resistive force that acts when one body rolls over another, e.g. a wheel on a road; it arises mainly from deformation at the contact patch.

Laws of friction:

(i) The magnitude of limiting (maximum static) friction, or of kinetic friction, is directly proportional to the normal reaction N between the two surfaces: f = mu*N, where mu is the coefficient of friction (mu_s for static, mu_k for kinetic). …