In the figure below a box (total mass = 1.65 kg) and another box (total mass =3.30 kg) slide down an inclined plane while attached b a massless rod parallel to the plane. The angle if incline is = 30.0°. The coefficient of kinetic friction between and the incline is =30.0°. The coefficient of kinetic friction between and the incline is = .226; that between and the incline is = .113. Compute the tension in the rod and the magnitude of the common acceleration of the two boxes.
Once the force vectors are labeled and the axis components are resolved we can set up Force Systems to compute the tension and magnitude of common acceleration. The systems are as follows:
System 1a: m1, perpendicular, a = 0
Force balance, .
System 1b: m1, parallel, a
System 2a: m2, perpendicular, a = 0
System 2b: m2, parallel, a
Since there is no acceleration in the vertical dimension we only add the horizontal systems for both masses to obtain of the system. This gives us: