Can someone show me how to do this dynamics question?

[Bebop]

I've been doing this question for a while but I can't seem to get the right answere. I end up with three unknowns and I can't see what I'm doing wrong.

Two particles A and B, of mass 8kg and 10kg respectively are connected by a light inextensible string which passes over a light smooth pulley P. Particle b rests on a smooth horizontal table and particle A rests on a smooth plane inclined at 30 degrees to the horizontal with the string taut and perpendicular to the line of intersection of the table and the plane as shown below.
The system is released from rest.
a) Find the magnitude of the acceleration of particle B
b) Find, in newtons, the tension in the string.
c) Find the distance covered by B in the first two seconds of motion, given B does not reach the pulley.

[arildno]

i)
Since the string is given to be inextensible, the magnitude of the accelerations of A og B must be the same; otherwise, the string would either contract or lengthen.

ii) The tension in the spring is equal in magnitude at all points on the spring.

Hence, you have basically two unknowns, particle acceleration and tension.

[Bebop]

Oh yes, I was stupid enough not to realise that the table was smooth so I though there was friction acting as well.

[arildno]

That wasn't a stupid reasoning from your side!
I think however, that if friction were intended to be included, the exercise would have given a value for the kinematic friction coefficient.(Otherwise, you wouldn't have been able to solve the problem..)

[flexten]

Three unknowns: well actually you have three knowns .. the forces on the block on the incline .. they must sum to zero, then solve for acceleration.
F1=gsintheta, F2=-m1a F3=-m2a=T

Best

[arildno]

Three unknowns: well actually you have three knowns .. the forces on the block on the incline .. they must sum to zero, then solve for acceleration.
F1=gsintheta, F2=-m1a F3=-m2a=T

Best


If you want to count every conceivable "unkown" in the problem, you've got 8:

2 vectorial particle accelerations (A total of 4 unknowns)
2 magnitudes of normal forces
2 tensile force magnitudes, each acting on a distinct block.