An elevator filled with passengers has a mass of 1683 kg. (a) The elevator accelerates upward from rest at a rate of 1.20 m/s2 for 2.75 s. Calculate the tension in the cable (in N) supporting the elevator. g

the tension is 18513N

Explanation:

Given that

mass = 1683kg

acceleration = 1.2m/s^2

acceleration due to gravity = 9.8m/s^2

T-mg = ma

T = ma + mg

T = m (a + g)

T = 1683 kg (1.20 m/s2 + 9.8)

T = 1683 (11)

T = 18513N

therefore, the tension is 18513N

T = 18.529 KN

Explanation:

We are given that;

Mass; m = 1683 kg

Upwards, acceleration; a = 1.2 m/s²

Downwards, acceleration due to gravity; g = 9.81 m/s²

Time; t = 2.75s

Now, The tension in the cable exerts a force up while gravity exerts a force down. The mass has an upward acceleration and thus, there are no horizontal forces.

We will take up as positive.

Thus,

Fnet is given as; F = T - W

W = mg while F = ma. and so,

ma = T - mg

Where t is Tension in cable.

Thus,

T = ma + mg

T = m (a + g)

T = 1683 (1.2 + 9.81)

T = 1683 (11.01) = 18529N = 18.529 KN