Question

An elevator filled with passengers has a mass of 1663 kg. (a) The elevator accelerates upward from rest at a rate of 1.20 m/s2 for 3.25 s. Calculate the tension in the cable (in N) supporting the elevator. 18317 Correct: Your answer is correct. N (b) The elevator continues upward at constant velocity for 8.92 s. What is the tension in the cable (in N) during this time

Answer 1

(a) T = 18309.63 N = 18.31 KN

(b) T = 16314.03 N = 16.314 KN

Step-by-step explanation:

(a)

The tension in an elevator while moving upward with some acceleration is given by the following formula:

`T = m(g+a)\\`

where,

T = Tension = ?

m = mass = 1663 kg

g = acceleration due to gravity = 9.81 m/s²

a = acceleration of elevator = 1.2 m/s²

Therefore,

`T = (1663\ kg)(9.81\ m/s^2 + 1.2\ m/s^2)\\`

T = 18309.63 N = 18.31 KN

(b)

Constant velocity means no acceleration. So, in that case, the tension will be equal to the weight of the elevator:

`T = mg\\T = (1663\ kg)(9.81\ m/s^2)\\`

T = 16314.03 N = 16.314 KN