# Thread: Mechanics help, resolving forces

1. ## Mechanics help, resolving forces

Two particles P and Q of equal mass are connected by a light inextensible string. The string passes over a small smooth pulley which is fixed at the top of a fixed wedge. One face of the wedge is smooth and inclined to the horizontal at an angle of 30° and the other face of the wedge is rough and inclined to the horizontal at an angle of 60°. Particle P lies on the rough face and particle Q lies on the smooth face with the string connecting them taut. The coefficient of friction between P and the rough face is 0.5.
a Find the acceleration of the system.
b Find the tension in the string.

for Q resolving vertically : T-mgcos60 = ma

for P, resolving horizontal : S = mgcos60

and resolving vertically for P : mg- t + mgcos30 = ma

mg = 2s

is this so far correct? Am not sure if these equation are correct, or what to do next?

Any help appreciated.

Thanks

2. ## Re: Mechanics help, resolving forces

forces acting on Q parallel to its incline ...

$T - mg\sin(30) = ma$

forces acting on P parallel to its incline ...

$mg\sin(60) - T - \mu mg\cos(60) = ma$

sum the two equations ...

$mg\sin(60) - mg\sin(30) - \mu mg\cos(60) = 2ma$

$\frac{g\sin(60) - g\sin(30) - \mu g\cos(60)}{2} = a$

calculate $a$ , then go back to either starting equation and calculate the tension force