An elevator cab and its load have a combined mass of 1600 kg. Find the tensions

Question

An elevator cab and its load have a combined mass of 1600 kg. Find the tensions in the supporting cable when the cab, originally moving downward at 12 m/s, is brought to rest with constant acceleration in a distance of 42 m. The figure shows two blocks connected by a cord (of negligible mass) that passes over a friction less pulley (also of negligible mass). The arrangement is known as Atwood's machine. One block has mass m_1 = 1.30 kg: the other mass m2 = 2.80 kg. What are the magnitude of the block's acceleration and the tension in the cord?

Explanation / Answer

here,

combined mass of elevator , m = 1600 kg

initial speed , u = 12 m/s

distance , s = 42 m

let the accelration be a

using third equation of motion

v^2 - u^2 = 2* a * s

0 - 12^2 = - 2 * a * 42

a = 1.71 m/s^2

let the tension in the string be t

t - m * g = m * a

t = 1600 * ( 9.8 + 1.71)

t = 18416 N

the tension in the string is 18416 N

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