Answer :
The shortest time in which the crane can lift the 7000 kg load a vertical distance of 120 meters, using only 65.0% of its maximum hoisting power, is approximately 98.2 seconds.
C) 98.2 s
To determine the shortest time in which the crane can lift the load, we can follow these steps:
Step 1: Convert the power of the motor from horsepower to watts.
Since 1 horsepower is equivalent to 745.7 watts, we can calculate the power in watts as follows:
Motor power (watts) = Motor power (hp) × Conversion factor
Motor power (watts) = 171 hp × 745.7 watts/hp
Motor power (watts) = 127521.7 watts
Step 2: Apply the safety factor to determine the usable power.
Since only 65.0% of the maximum power can be used, we can calculate the usable power as follows:
Usable power (watts) = Motor power (watts) × Safety factor
Usable power (watts) = 127521.7 watts × 0.65
Usable power (watts) ≈ 82889.105 watts
Step 3: Calculate the work required to lift the load.
Work is calculated by multiplying the force required to lift the object by the distance it is lifted. In this scenario, the force is equal to the weight of the load, which is the mass multiplied by acceleration due to gravity (9.81 m/s²):
Work (joules) = Force (newtons) × Distance (meters)
Work (joules) = Load mass (kg) × Gravity (9.81 m/s²) × Lift distance (m)
Work (joules) = 7000 kg × 9.81 m/s² × 120 m
Work (joules) = 7000 kg × 9.81 m/s² × 120 m
Work (joules) = 8211600 joules
Step 4: Calculate the shortest time to lift the load using the usable power.
Power is defined as the rate at which work is done, or equivalently, work divided by time. Therefore, we can determine the shortest time by dividing the work needed by the usable power:
Shortest time (seconds) = Work (joules) / Usable power (watts)
Shortest time (seconds) = 8211600 joules / 82889.105 watts
Shortest time (seconds) ≈ 99.06 seconds
From the given options, the closest to 99.06 seconds is (C) 98.2 seconds. Therefore, the shortest time in which the crane can lift the 7000 kg load a vertical distance of 120 meters, using only 65.0% of its maximum hoisting power, is approximately 98.2 seconds.
