CBSE Class 11-science Answered

what are the derivations that are there in laws of motion .explain them.

Asked by ABHILASHA | 16 Sep, 2019, 06:54: PM

Expert Answer

(1) F = m a

Above relation is derived from Newton's second law.

This relation express that force acting on a body is proportional to acceleration produced by that force.

Force and acceleration are vector quantities. Direction of force is same as the direction of acceleration

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(2) Conservation of momentum

In an isolated system (i.e. a system with no external force), mutual forces between pairs of particles in the system can cause momentum
change in individual particles, but the total momentum remains unchanged.

Consider two bodies of respective initial momentum P_A and P_B .

Let them collide and their momentum changes after collision as given by P_A' and P_B' .

Then by conservaton of momentum, P_A + P_B = P_A' + P_B'

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(3) when an object moves in a circular path, it experiences acceleration along the radial direction and

the force due to this acceleration is known as centripetal force. Slipping away from the circular path is prevented

by friction force acting at the contact surface upto maximum speed v_max . This maximum speed is given by,

begin mathsize 14px style v subscript m a x end subscript space equals space square root of mu subscript s space R space g end root space end style

As per the above relation friction between the contact surface plays the vital role to prevent the slipping away

from the circular path of an object when the object is performing circular motion.

But friction may not be desirable. For example , if friction alone is utilised for vehicles , wheel and tyres will be damaged due to friction.

Hence banking is done on the turning of the road where the path is partially circular.

Banking of road means, small amount of slope is maintained from one end to other end across the width of the road.

On a banked road with slope tanθ, maximum safe speed v_max is given by,

begin mathsize 14px style v subscript m a x end subscript space equals space square root of R space g space cross times fraction numerator mu subscript s plus space tan theta over denominator 1 space minus space mu subscript s tan theta end fraction end root end style

when there is no friction at contact surface, i.e., μ_s = 0, safe speed limit

begin mathsize 12px style v subscript o space equals space square root of R space g space tan theta end root end style

Answered by Thiyagarajan K | 18 Sep, 2019, 10:43: PM

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