As per the question the weight of the elevator is 14,700 N.
The weight of a substance is the product of mass and acceleration due to gravity or we may say it is the force with which earth attracts any body towards its centre.
The acceleration due to gravity g = 9.8 m/s^2
Hence force of gravity=weight
[tex]i.e\ \ F_{g} = m*g[/tex] [ m stands for mass]
[tex]m=\frac{F_{g}} {g}[/tex]
[tex]m=\frac{14700}{9.8} kg[/tex]
[tex]m=1500 kg[/tex]
The acceleration of the accelerator[a] [tex]=\ -0.30m/s^2[/tex]
It means the elevator is decelerating.
As per the free body diagram, the weight of elevator is in vertically downward direction.
The force of tension [tex][F_{t} ][/tex] is in vertically upward direction.
Hence the net force acting on the elevator is [tex]F_{g} -F_{t}[/tex]
As per Newton's law's of motion the net force [tex][F_{net} ]= ma[/tex]
[tex]i.e\ F_{g} -F_{t} = ma[/tex]
[tex]F_{t} =F_{g} -ma[/tex]
[tex]= 14,700- 1500*[-0.30] N[/tex]
[tex]=[14,700+450] N[/tex]
[tex]=15,150 N[/tex] [ANS]
Hence the correct option is D i.e 15,150 N.
