Question

A lift, mass 250 kg. is initially at rest on the ground floor of a tall building. Passengers with an unknown total mass, m. climb into the lift. The lift accelerates upwards at 1.6 ms. The cable supporting the lift exerts a constant upward force of 7700 N. Use g= 10 ms. What is the maximum mass, m. of the passengers the lift can carry in order to achieve a constant upward acceleration of 1.6 ms ?. (A) 770 kg (B) 413.79 kg (C)4812.5 kg (D)663.79 kg (E) None of these​

Answer 1

I think the acceleration is 1.6 m/s²

Okay lets begin

The total mass present in the lift (along with the lift) = 250 + m

Force exerted by the cable = 7700 N

if this force is responsible for an acceleration of 1.6 m/s²

then

as the lift moves up a pseudo force is also activated

thus (250+m)(g+a) = 7700

(250+m)(9.8+1.6) = 7700

250+m =  7700/ 11.4  = 675.43

250+m = 675.43

thus

m= 675.43 - 250 = 425.43

although matches near to 413.79

still i think you must go with

(E) NONE OF THESE