Answer :
The time required for the lift is approximately 16.74 seconds when a 7.06-hp motor lifts a 243-kg beam directly upward at a constant velocity from the ground to a height of 37.1 m.
To solve this problem, we can use the formula:
Work = Force x Distance
Power = Work / Time
Velocity = Distance / Time
First, let's calculate the force required to lift the beam:
Force = Weight x Acceleration due to gravity
Force = [tex]243 kg * 9.8 m/s^2[/tex]
Force = 2381.4 N
Next, let's calculate the work done by the motor:
Work = Force x Distance
Work = 2381.4 N x 37.1 m
Work = 88,241.94 J
Now, we can use the power of the motor to find the time required for the lift:
Power = Work / Time
Time = Work / Power
Power = 7.06 hp x 746 W/hp
Power = 5,267.76 W
Time = 88,241.94 J / 5,267.76 W
Time = 16.74 s
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