Question

A 9.0 kg block is held by a pulley system shown in Fig. What force must the
person exert in the following cases ?
(a) to hold the block at rest;
(b)to lower it at 2 m/s ;
(c)to raise it with an acceleration of 0.5 m/s2?
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Answer 1

so if you want it to lower at a constant speed the acceleration must be zero..initially choose the force such that the velocity reaches 2m/s, like apply 40.5 N tension so it will give an acceleration of 1m/s.Now continue it for 2s so by v=u+at you get a velocity of 2m/s if it was initially at rest.Now change the tension to 45N instantaneously, hence no acc. thereafter lowering it at the desired speed.