Two masses are connected by a string which passes over a frictionless, mass less

Question

Two masses are connected by a string which passes over a frictionless, mass less pulley. One mass hangs vertically and one mass slides on a 30 degrees incline. The vertically hanging mass is 6.0 kg and the mass on the incline is 4.0 kg. The acceleration of the 4.0 kg mass is,

The answer is 3.92 m/s.

When setting up components for the mass on the incline this is what I got...

x:mgsin +T = ma

y: -T+ mg = ma

I understand that the positive forces will be in the same direction as acceleration...but then why would the correct x component be:

x: -mgsin + T=ma

I thought there was NO friction.

Explanation / Answer

If we consider the direction of acceleration of the block to up the incline,
then we while writing the equation of motion , we write the forces which are in same direction as acceleration to be positive and the one in opposite direction to be negative,

Here tension T is in same direction, whereas mgsin acts down the slope, and is negative

hence, we have

ma = T - mgsin

Cheers !!

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