An elevator cab that weighs 27.8 kN moves upward. What is the tension in the cable if the cab's speed is (a) increasing at a rate of 2 1.22 / msand (b) decreasing at a rate of 2 1.22 / ms?

a) T = 8.63 * 10 ⁴ N, b) T = - 3.239 * 10 ⁴ N

Explanation:

Given:

W = 27.8 KN = 27.8 * 10 ³ N,

For upward motion: Fnet is upward, Tension T is upward and weight W is downward so

a) a=21.22 m/s² (not written clearly the unit. if it is acceleration?) then

Fnet = T - W

⇒ T = F + W = ma + W

T = (W/g) a + W (W=mg ⇒m=W/g)

T = (27.8 * 10 ³ N / 9.8) 21.22 m/s² + 27.8 * 10 ³ N

T = 86,263.265 N

T = 8.63 * 10 ⁴ N

b) For Declaration in upward direction a = - 21.22 m/s²

Fnet = T - W

⇒ T = F + W = ma + W

T = (W/g) a + W

T = (27.8 * 10 ³ N / 9.8) (-21.22 m/s²) + 27.8 * 10 ³ N

T = - 32395.5 N

T = - 3.239 * 10 ⁴ N

as Tension can not be negative I hope the value of acceleration and deceleration is correct.