At a given instant,block A is moving with a v | vedclass

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(A) Let the upward direction be positive and the downward direction be negative.For block $A$,the velocity is $v_A = +5\,m/s$.The string is connected

Vedclass · Accepted Answer

$15\,m/s \downarrow$

Vedclass · Answer

(A) Let the upward direction be positive and the downward direction be negative.For block $A$,the velocity is $v_A = +5\,m/s$.The string is connected to block $A$ at two points and passes through a movable pulley attached to $A$. Let the length of the string be $L$.By the constraint relation for the string length,the sum of the velocities of the points connected to the string must be zero.There are three segments of the string that change length as $A$ and $B$ move. If $A$ moves up by $x$,the three segments connected to the pulley system shorten by $x$ each,while the segment connected to $B$ lengthens by the displacement of $B$.Using the velocity constraint: $v_A + v_A + v_A + v_B = 0$.Substituting $v_A = 5\,m/s$: $5 + 5 + 5 + v_B = 0$.$15 + v_B = 0$.$v_B = -15\,m/s$.The negative sign indicates that block $B$ is moving downwards with a velocity of $15\,m/s$.

At a given instant,block $A$ is moving with a velocity of $5\,m/s$ upwards. What is the velocity of block $B$ at that instant?

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