1. prove that angle of repose is equal to angle of friction

2. prove that 2nd law of motion is the real law of motion. (what is real law of motion)

Here angle BAC=α =angle of repose

Now from the figure, the forces involved are weight mg of the body acting vertically downwards,normal reaction R acting perpendicular to AB,Force of friction F,acting up the plane AB.

Resolving 'mg' into rectangular components we have: mgsinα and mgcosα

In equilibrium: F=mgsinα,---(i)

R=mgcosα---(ii)

Dividing (i) by (ii),we get F/R=tanα

and we know that coefficient of friction=F/R

Therefore coefficient of friction =tanα

(2)

Newton's Second Law can be sued to derive both the First and Third Laws

**Derivation of the 1** ^{st }**law of mortion from the 2** ^{nd }**law:**

According to Newton’s 2 ^{nd }law of motion,

F = ma

Where, F is the force applied, m is the mass of the body and a is the acceleration of the body.

So,

In absence of a force,

F = 0

=> ma = 0

=> a = 0

Since, m cannot be zero for a body.

Zero acceleration means, body at rest will remain at rest and a body in uniform motion will continue its uniform motion. Which is Newton’s 1 ^{st }law of motion.

--

**Derivation of 3** ^{rd }**law from 2** ^{nd }**law:**

Consider an isolated system of two bodies A and B. An isolated system is such that no force acts on the system.

**
**