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M1 Dynamics questions

10) Two particles P and Q of masses 1kg and 2kg respectivly are hanging vertically form the ends of alight inextensible string whihc passes over a smooth fixed pulley. The system is released from rest wtih both particels a distance of 1.5m above the floor. When the masses have been moving for 0.5s the string breaks. Find the further time that elapses before P hits the floor.

Reply 1

TheDuck

insparato

For the first 0.5s, F=ma
so 2g-g=a, so a=g (upwards).
s=ut+0.5at²
so distance travelled upwards=0.5*g*0.5²
=g/8
speed upwards=g/2
So time before P hits ground satisfies (now taking downwards as positive to confuse matters)
s=ut²+0.5at²
1.5+g/8=-gt/2+gt²
And then use the quadratic formula to solve t and take the positive answer obviously.

I then get t=0.834s