If the power rating of the motor is 8x10^4 Watts and our equation for Power is:
[tex]Power=\frac{Energy}{time}=\frac{Work}{time}=\frac{Force \times Displacement}{time}\\\\P=Force \times Velocity[/tex]
Note that:
[tex]F=ma=mg[/tex]
where g is the average gravity on Earth which is approximately 9.8 m/s^2.
And so:
[tex]P=F \times V\\P=m \times g \times V\\\\\ m=\frac{P}{gv} \\\\[/tex]
[tex]m=\frac{8.1 \times 10^4 }{9.8 \times 3} =2755.1kg[/tex]
In terms of force:
[tex]F=mg=2755.1kg \times 9.8 \frac{m}{s^2}=27000N[/tex]
The maximum weight of motor that can lifted at the given speed is of 27000 N.
Given data:
The maximum power rating of the motor is, [tex]P = 8.1 \times 10^{4} \;\rm W[/tex].
The weight of elevator is, [tex]W = 1.8 \times 10^{4} \;\rm N[/tex].
The speed of motor is, v = 3.0 m/s.
Since, the power rating of motor is obtained due to the force experienced on the elevator. Then,
[tex]P = F \times v[/tex]
Solving as,
[tex]8.1 \times 10^{4} = F \times 3.0 \\F = 27000 \;\rm N[/tex]
Now, the force experienced on the elevator is due to the weight of motor. Then,
Force (F) = Weight of motor (W')
[tex]27000 = W' \\\\W' = 27000 \;\rm N[/tex]
Thus, we can conclude that the maximum weight of motor that can lifted at the given speed is of 27000 N.
Learn more about the power here:
https://brainly.com/question/12584580
