Question

3. Derivee the expression for tension in string and acceleration for connected motion of two object with string​

Answer 1

Answer:

Explanation:Let masses m1 and m2 are hanging on two sides of pulley. Let mass of string is negligible and the string is instretcheable.

Let us assume friction in the pulley is negligible.

Let m2 > m1 , so that mass m2 is moving downwards and m1 is moving upwards.

Tension forces acting on the string are shown in figure.

Let a be the acceleration of the system.

Let us apply Newton's second law to m2 :- ( m2 g ) - T = m2 a .(1)

Let us apply Newton's second law to m1 :- T - ( m1 g ) = m1 a ..(2)

By adding eqn.(1) and (2), we get ( m1 + m2 ) a = ( m2 - m1 ) g

Hence acceleration a = [ ( m2 - m1 ) / ( m1 + m2 ) ] g .(3)

Tension in the string is obtained from eqn.(2) as, T = m1 ( g + a ) .(4)

By substituting for acceleration from eqn.(3), Tension in the string is obtained from eqn.(4) as

T = [ (2 m1 m2 ) / ( m1 + m2 ) ] g