Calculating Acceleration of Particles on a Sloping Roof

[hendrix7]

Two particles, A (mass 0.2 kg) and B (mass 0.3 kg), are attached to an inexstensible string which passes over a smooth pulley. A initially rests on a sloping roof that makes a 30 degree angle with the horizontal and B hangs freely below the roof. Find the acceleration, a, of the particles when released from rest.
(I tried to draw a diagram but it came out looking a mess).
My workings (T is the tension in the string):
(1) 0.3g - T = 0.3a
(2) T - 0.2g sin 30 deg = 0.2a

(1) T = 0.3g - 0.3a
(2) 0.3g - 0.3a - 0.1g = 0.2a
(2) 0.5a = 0.2g
(2) a = 0.4g
taking g to be 9.8 m/s/s:
a = 3.92 m/s/s
My book says 7.84 m/s/s.
What did I do wrong?

Thanks for any help.
Jimi

 

[OlderDan]

My book says 7.84 m/s/s.
What did I do wrong?

Thanks for any help.
Jimi

Try sloping your roof in the other direction. Looks like that would just about give the quoted answer, but I did not calculate it

 

[ramollari]

According to OlderDan's tip you should replace eq [2] by

T + 0.2gsin30^{\circ},

which should give you 4/5g.

 

[hendrix7]

Yep, you're both right, I see it. Thanks.