Equation of motion of lift:

Write equation of motion of lift when move up and when move down 

Assume,

W = Weight carried by lift m = Mass carried by lift = W/g
a = Uniform acceleration

T = Tension in cable supporting lift, also called as Reaction of the lift

For UP MOTION

Net force in upward direction = T-W Also Net Force = m.a

That is        T-W = m.a                                                                                                                                       ...(i) FOR DOWN MOTION

Net force = W - T

Also Net Force = m.a That is

W - T = m.a                                                                                                                                     ...(ii)

Note: Wave taken weight or mass carried by lift only. We have assumed that weight carried by lift includes weight of lift also. But sometimes example contains weight of the lift and weight carried by lift separately. The weight carried by the lift or weight of the operator etc, will exert pressure on the floor of the lift. Whereas tension in cable will be given by algebraic sum of the weight of the lift and weight carried by lift.