Answer:
14060 N
Explanation:
We start by calculating the acceleration of the elevator. This can be found using the suvat equation:
[tex]v^2-u^2=2as[/tex]
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
[tex]a=\frac{v^2-u^2}{2s}=\frac{0-(12)^2}{2(26)}=-2.77 m/s^2[/tex]
Now let's write the equation of the forces acting on the elevator. Taking upward as positive direction:
[tex]T-mg=ma[/tex]
where
T is the tension in the cable
(mg) is the weight of the elevator, where
m = 2000 kg is the mass
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]a=-2.77 m/s^2[/tex] is the deceleration
Solving for T,
[tex]T=m(g+a)=(2000)(9.8-2.77)=14060 N[/tex]
