Final answer:
To calculate the time it takes for the motor to raise the section of the boiler, we can use the equation: work = force × distance. First, calculate the force by multiplying the weight of the section by the acceleration due to gravity. Next, convert the distance to meters. Finally, use the work and power equations to calculate the time.
Step-by-step explanation:
To calculate the time it takes for the motor to raise the section of the boiler, we can use the equation:
work = force × distance
The work done by the motor is equal to the force applied by the motor multiplied by the vertical distance the section is raised. The force can be calculated using the weight of the section, which is equal to its mass multiplied by the acceleration due to gravity. The distance is given as 38 ft, which can be converted to meters.
First, let's calculate the force:
Weight = mass × acceleration due to gravity
Weight = 475 lb × 9.8 m/s2
Force = Weight = (475 lb × 9.8 m/s2) / (2.2046 lb/kg)
Next, let's convert the distance to meters:
Distance = 38 ft × 0.3048 m/ft
Now, we can calculate the work done:
Work = force × distance
Finally, we can use the work and power equations to calculate the time:
Power = work / time
Time = work / power
Since power is given in horsepower (hp) and time is required in seconds, we need to convert horsepower to watts (1 hp = 745.7 watts) and divide by the power factor (typical value is around 0.8) to account for inefficiencies. Once we have the power in watts, we can use the power equation to calculate the time.
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