An elevator lifts a total mass of 1.1 x 10^3 kg, a distance of 40 m in 12.5s. How much power does the elevator demonstrate?
Power = M g H / t
= 1100* 9.8*40/12.5 watts
= 34,500 W
= 46 Horsepower
To calculate the power demonstrated by the elevator, we can use the equation:
Power = Work / Time
First, we need to calculate the work done by the elevator. The work done is equal to the force applied multiplied by the distance moved.
Work = Force * Distance
To calculate the force applied by the elevator, we can use Newton's second law of motion, which states that Force = Mass * Acceleration.
In this case, the elevator is moving at a constant velocity, so the acceleration is zero. Thus, the force applied by the elevator is:
Force = Mass * Acceleration
= 1.1 x 10^3 kg * 0
= 0 N
Since the force applied is 0 N, the work done by the elevator is also 0 J (Joules) because any amount of work multiplied by 0 is 0.
Now that we know the work done is 0 J, we can calculate the power demonstrated by the elevator using the equation:
Power = Work / Time
= 0 J / 12.5 s
= 0 W (Watts)
Therefore, the elevator demonstrates 0 Watts of power.
To find the power demonstrated by the elevator, we can use the formula:
Power = (Work Done) / (Time)
The work done can be calculated using the formula:
Work Done = Force x Distance
First, we need to calculate the force experienced by the elevator. We can use Newton's second law of motion:
Force = Mass x Acceleration
Acceleration can be calculated using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Since the elevator is moving vertically, we can assume the initial velocity is zero.
Given:
Mass (m) = 1.1 x 10^3 kg
Distance (d) = 40 m
Time (t) = 12.5 s
Step 1: Calculate Acceleration
Acceleration = (Final Velocity - Initial Velocity) / Time
Since the initial velocity is 0,
Acceleration = (Final Velocity - 0) / Time
Since Distance = (Initial Velocity x Time) + (0.5 x Acceleration x Time^2)
And Distance = 40 m
40 m = (0 x 12.5) + (0.5 x Acceleration x (12.5)^2)
40 m = (0.5 x Acceleration x 156.25)
40 m = 78.125 x Acceleration
Acceleration = (40 m) / (78.125)
Acceleration = 0.512 m/s^2
Step 2: Calculate Force
Force = Mass x Acceleration
Force = (1.1 x 10^3 kg) x (0.512 m/s^2)
Force = 563.2 N
Step 3: Calculate Work Done
Work Done = Force x Distance
Work Done = (563.2 N) x (40 m)
Work Done = 22,528 J (Joules)
Step 4: Calculate Power
Power = Work Done / Time
Power = 22,528 J / 12.5 s
Power = 1802.24 W (Watts)
Therefore, the elevator demonstrates a power of 1802.24 Watts.