Question

To paint the side of a building, paainter normally hoists himself up by pulling on the rope $A$ as in figure. The painter and plateform together weigh $200N$ The rope $B$ can withstand $300N$. Then (i)The maximum acceleration that painter can have upwards is
5m/s${}^2$
(ii)To hoist himself up , rope B must withstand minimum 400 N force .

Answer 1

For maximum acceleration tension in string B should be maximum which is $300N$ which gives value of $T$ in string $A=150N$

now writing equation for platform + painter we get

$2T-200=20a$...(1)

using $T$ we get value of $a=\frac{100}{20}=5\frac{m}{s^2}$

(1) If a=0, then from eq 1 we get $T=\frac{200}{2}=100N$

(2) If $a=2\frac{m}{s^2}$ ,from eq 1 we get, $T=\frac{(40+200)}{2}=120N$