m1

Block of mass 4kg rests on a smooth plane inclined at 20 deg to horizontal. It is connected by a light, inextensible string passing over a smooth pulley at the top of the slop at a 3kg particle hanging freely. Find the acceleration of the system and the tension in the string.

Ok so I started with:

F=ma

a=f(total)
M(total)

3*9.8 + 4*9.8sin20 = a
3+4

am I on the right track of how to get the acceleration?

Where's the tension gone from your equations?

You basically want
motion of block: weight acting down the slope against tension pulling up, giving mass x acceleration for the block

and motion of particle: weight downwards acting against tension upwards, resultant gives mass x acceleration.for particle.

Since everything is smooth and the string is inextensible the tensions and accelerations are the same in each case.

ahh

so you mean

T-Mg sin20=ma

T-Mg= -ma

I'm not sure why you're mixing up M's and m's here.

The mass in the first equation should be the mass of the block on both sides; the mass in the 2nd equation should be the mass of the particle on both sides. Also it's simpler to write the 2nd one as mg - T = ma since the net movement is downwards, although it doesn't affect the arithmetic.