Find the scale reading?

Question

A person with mass of 55 kg is standing on a scale in an elevator. The elevator is moving up and accelerating at 1.5 m/s^2 for 3 seconds, then continues with constant speed. Find the scale reading a) before starting to move, b) when accelerating, c) when moving at constant speed?

Answer 1

Sum of the forces in the vertical direction F_y = F_N + (-mg) = ma

 

(a) At rest, ma= 0.

Scale reading is equal to F_N and is equal to (mg)

F_N = 55kg *(9.8m/s) = 539 N = 121 lbs

 

(b) at a=1.5m/s², 

F_N = mg + ma = (55kg)(9.8m/s²) + (55kg)(1.5m/s²) = 621.5 N = 140 lbs

 

(c) at constant speed, a = 0,

same as (a) scale reading is equal to F_N = 539 N = 121 lbs