What distance will a 10 hp motor lift a 2000 lb elevator in 30 s? What was the average velocity of this elevator during the lift?
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To determine the distance the 10 hp motor will lift the 2000 lb elevator in 30 s, we can use the following formula:
Work = Force x Distance
First, let's convert the horsepower (hp) to a more standard unit like watts (W).
1 hp is approximately equal to 746 W.
So, 10 hp = 7460 W (10 multiplied by 746).
Next, let's find the work done by the motor.
Work = Power x Time
Work = (7460 W) x (30 s) = 223,800 joules (J)
To find the distance, we need to rearrange the formula:
Distance = Work / Force
Given that the force is the weight of the elevator, we can use the following formula:
Force = mass x acceleration due to gravity
Mass is given as 2000 lb. To convert it to kilograms (kg), we need to divide by the conversion factor 2.205 lb/kg.
So, the mass of the elevator is: 2000 lb / 2.205 lb/kg = 907.18 kg (rounded to two decimal places).
The acceleration due to gravity is approximately equal to 9.8 m/s^2.
Force = (907.18 kg) x (9.8 m/s^2) = 8895.92 N (rounded to two decimal places)
Now, we can calculate the distance:
Distance = 223800 J / 8895.92 N = 25.16 m (rounded to two decimal places)
Therefore, the 10 hp motor will lift the 2000 lb elevator a distance of approximately 25.16 meters in 30 seconds.
To find the average velocity of the elevator, we can use the formula:
Average velocity = distance / time
Average velocity = 25.16 m / 30 s = 0.84 m/s (rounded to two decimal places)
Hence, the average velocity of the elevator during the lift is approximately 0.84 meters per second.