Answer:
The upward acceleration of the elevator is 10.51 m/s²
Step-by-step explanation:
Given;
weight on Earth while stationary, W = 550 N
apparent weight when the elevator accelerates upwards, W'₁ = 590 N.
apparent weight when the elevator descends, W''₂ = 510 N
When moving upwards;
T = ma + mg
where T is the total reading on the scale of the elevator
T = ma + W
W'₁ = ma + W
590 = ma + 550
ma = 590 - 550
ma = 40-----------equation (i)
where;
m is your mass
a is your acceleration
When descending;
T = mg - ma
T = W - ma
W''₂ = W - ma
510 = 550 - ma
ma = 550 - 510
ma = 40 ----------------equation (ii)
Now, ma is the same in both equations, we calculate m first,
From Newtons second law of motion;
F = W = mg
when you are stationary on Earth, g = 9.8 m/s²
550 = 9.8 x m
m = 550/9.8
m = 56.123 kg
Finally, substitute m in any of the equations;
56.123 x a = 40
a = 40/56.123
a = 0.71 m/s²
When moving upwards;
the acceleration of the elevator becomes = (a + g)
= (0.71 + 9.8)
= 10.51 m/s²