I'm designing a lifting device powered by a motor, i would like to know if the forces exerted by the load on pulley 1 and 2 are equal when the motor star running , or if in pulley 1 is exerted more force because the location of the load at the end of the lifting platform. The lifting platform only moves vertically, restricted by rails. What I want to know if the load will exert a perpendicular force that could create friction on the rails
Of course the load will exert a moment, to study the behaviour of your system you can simply model it as a constrained beam in pure bending if the elasticity of your platform is not negligible or as a constrained rigid body. Every point of the rail is a constrained point, analyzing the strain diagrams you can compute how much perpendicular force you will have.
The drawing is lacking detail on how to the load and platform will not rotate. Despite this, you can assume accelerations are zero; therefore static. The sum of the forces, and the sum of the moments in the system must equal zero. Then a safety factor of should be computed per ASME B30.