Question

TWO MASSES ARE CONNECTED BY A STRING PASSING OVER A PULLEY ACCELERATING UPWARD.IF A1 AND A2 BE THE ACC. OF THE TWO BODIES THEN , FIND THE RELATION BETWEEN A,A1 AND A2.

Answer 1

Answer on Question #40893 – Physics – Mechanics

TWO MASSES ARE CONNECTED BY A STRING PASSING OVER A PULLEY ACCELERATING UPWARD. IF A1 AND A2 BE THE ACC. OF THE TWO BODIES THEN, FIND THE RELATION BETWEEN A, A1 AND A2.

Solution:

$a_1$ – acceleration of the first body;

$a_2$ – acceleration of the second body;

$a$ – acceleration of the pulley;

This acceleration of the pulley is in upward direction. Therefore a pseudo force will act on both the masses in the downward direction.

Be extremely careful to note that $a'$ is the acceleration of $m_1$ and $m_2$ in the pulley frame of system and NOT the inertial frame which is the ground. We can write equation of motion for both masses and solve for $a'$ and $T$.

Now we have to find $a_1$ and $a_2$ which are their acceleration in the ground frame of reference. Now the entire system is going upwards with $a$.

$m_1$ is moving upward with $a$ and downwards with $a'$

So its total downward acceleration will be $a_1 = a' - a$

Mass $b$ is moving upwards with $a$ and upwards with $a'$

So its total upwards acceleration will be $a_2 = a' + a$

Relations between $a_1, a_2$ and $a$:

$$a_1 = a' - a$$ $$a _ {2} = a ^ {\prime} + a$$

Answer: $a_1 = a' - a$

$$a _ {2} = a ^ {\prime} + a$$