Physics: An elevator and its load have a combined mass of 2000 kg. find the tension in the supporting cable when the elevator, originally moving downward at 12 m/s, is brought to rest with constant acceleration in a distance of 26 m.3

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An elevator and its load have a combined mass - id203410909, chevysilveradofixit

math9878

07.01.2022

14060 N

Explanation:

We start by calculating the acceleration of the elevator. This can be found using the suvat equation:

v^2-u^2=2as

where

v = 0 is the final velocity

u = 12 m/s is the initial velocity

a is the acceleration

s = 26 m is the stopping distance

Solving for a, we find

$a=\frac{v^2-u^2}{2s}=\frac{0-(12)^2}{2(26)}=-2.77 m/s^2$

Now let's write the equation of the forces acting on the elevator. Taking upward as positive direction:

T-mg=ma

where

T is the tension in the cable

(mg) is the weight of the elevator, where

m = 2000 kg is the mass

g=9.8 m/s^2 is the acceleration of gravity

a=-2.77 m/s^2 is the deceleration

Solving for T,

T=m(g+a)=(2000)(9.8-2.77)=14060 N

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