A passenger weighing 800 N is inside an elevator weighing 25000 N that rises 30 m in exactly 1 min. How much power is needed for the elevator's trip?
power = work/time
= (25000+800)(30)/60
= 12,900 Watts or about 13 KW
2500
To calculate the power needed for the elevator's trip, we need to know the work done and the time it takes to do that work.
Work (W) is defined as the force applied over a distance. In this case, the force is the weight of the passenger and elevator, and the distance is the height the elevator rises.
The work done (W) is calculated by multiplying the force (F) by the distance (d):
W = F × d
In this case, the force is the combined weight of the passenger and elevator:
F = 800 N (weight of the passenger) + 25,000 N (weight of the elevator) = 25,800 N
The distance is given as 30 m.
Now, we need to calculate the work done by substituting the values into the formula:
W = F × d = 25,800 N × 30 m = 774,000 J (joules)
Next, we need to calculate the time taken for the trip, which is given as 1 minute. However, power is typically measured in watts, which is the amount of work done per unit of time. Therefore, we need to convert 1 minute into seconds:
1 minute = 60 seconds
Now, we can calculate the power (P) by dividing the work (W) by the time (t):
P = W / t
Substituting the values:
P = 774,000 J / 60 s = 12,900 W (watts)
Therefore, the power needed for the elevator's trip is 12,900 watts.