How long would it take a 20.0 hp motor to lift a 1,000.0 kg crate from the bottom of a freight's hole deck(40.0m)?
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To calculate the time it would take for the motor to lift the crate, we can use the formulas for work and power.
First, let's find the work done to lift the crate. The work (W) is given by the equation:
W = mgh
Where:
W = Work done (in joules)
m = Mass of the crate (in kilograms)
g = Acceleration due to gravity (approximately 9.8 m/s^2)
h = Height lifted (in meters)
Plug in the values:
m = 1000.0 kg
g = 9.8 m/s^2
h = 40.0 m
W = 1000.0 kg * 9.8 m/s^2 * 40.0 m
W = 392000 joules
Now, let's calculate the time (t) using the power (P) equation:
P = W / t
Where:
P = Power (in watts)
W = Work done (in joules)
t = Time taken (in seconds)
Given:
P = 20.0 hp
1 horsepower (1 hp) is approximately equal to 746 watts, so we can convert it:
P = 20.0 hp * 746 watts/hp
P = 14920 watts
Plug in the values:
14920 watts = 392000 joules / t
Now, let's solve for t:
t = 392000 joules / 14920 watts
t ≈ 26.24 seconds
Therefore, it would take approximately 26.24 seconds for the 20.0 hp motor to lift the 1,000.0 kg crate from the bottom of the freight's hole deck.