Answer to Question #267311 in Physics for shadid

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 m/s−2. The cable supporting the lift exerts a constant upward force of 7700 N. Use g = 10 m/s−2. 

1. Draw a labeled force diagram indicating all the forces acting on the lift while it accelerates upwards.

2. What is the maximum mass, m, of the passengers the lift can carry in order to achieve a constant upward acceleration of 1.6 m/s−2.

Answer 1

1.

2. $F-(250+m)g=(250+m)a\to 7700-(250+m)\cdot10=(250+m)\cdot1.6\to$

$m=413.79\ (kg)$