Question

An object of mass 2kg on a plane inclined at angle 40degree and whose coefficient of dynamic friction is 0.3 is connected to another mass of 1kg which hangs vertically over a frictionless pulley. Obtain the acceleration of the system

Answer 1

First find Fn on the 2 kg mass. Net force along an axis perpendicular to the ramp surface is 0, so:
Fn + Fgcos40 = 0
Fn + (-9.81)(2)cos40 = 0
Solve for Fn

Now work out net force of system:
Fa + Fgsin40 + Fk
= 9.81(1) + (-9.81)(2)sin40 + (0.3)(Fn)
Plug in Fn that you found above to get net force of the system.

Divide net force by total mass of system (3kg) to get system acceleration.