How long would it take a 20.0 hp motor to lift a 1,000.0 kg crate from the bottom of a freighter's hold to the deck (40.0 m)?
The work required is
M*g*H = 1000*9.81*40 = 3.92*10^5 Joules
A 20 HP motor can provide 20*746 = 14,920 watts (J/sec) of power.
Time= Work/Power
I get 26.3 seconds
To calculate the time it takes for a motor to lift a crate, we need to apply the concept of work and power.
First, we need to determine the work done to lift the crate. The work (W) is given by the formula: W = force × distance.
The force required to lift the crate can be calculated using Newton's second law of motion: F = m × g, where m is the mass of the crate (1,000.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
So, F = 1,000.0 kg × 9.8 m/s² = 9,800.0 N.
The distance traveled is 40.0 m.
Therefore, the work done is: W = 9,800.0 N × 40.0 m = 392,000.0 N·m (also known as Joules).
Next, we can calculate the power (P) of the motor using the formula: P = work / time.
Since we are given the power of the motor as 20.0 hp (horsepower), we need to convert it to watts (W) for consistency. One horsepower is equal to approximately 746 watts.
So, P = 20.0 hp × 746 W/hp = 14,920 W.
Now, we can rearrange the power formula to solve for time (T):
T = work / power
T = 392,000.0 N·m / 14,920 W ≈ 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 freighter's hold to the deck.