How much energy does a 5hp motor deliver in 2 hours. Answer should be in MJ
The Correct Answer and Explanation is:
To find how much energy a 5 horsepower (hp) motor delivers in 2 hours, we first need to convert horsepower to watts and then calculate the energy in megajoules (MJ).
Step 1: Convert horsepower to watts
1 horsepower (hp) is equal to 745.7 watts (W). Therefore, a 5 hp motor delivers:5 hp×745.7 W/hp=3728.5 W5 \, \text{hp} \times 745.7 \, \text{W/hp} = 3728.5 \, \text{W}5hp×745.7W/hp=3728.5W
Step 2: Calculate the total energy delivered in 2 hours
The energy delivered by the motor is given by the formula:Energy (J)=Power (W)×Time (s)\text{Energy (J)} = \text{Power (W)} \times \text{Time (s)}Energy (J)=Power (W)×Time (s)
We need to convert the time to seconds. There are 3600 seconds in an hour, so in 2 hours:2 hours=2×3600 seconds=7200 seconds2 \, \text{hours} = 2 \times 3600 \, \text{seconds} = 7200 \, \text{seconds}2hours=2×3600seconds=7200seconds
Now we can calculate the total energy:Energy (J)=3728.5 W×7200 s=26,821,200 J\text{Energy (J)} = 3728.5 \, \text{W} \times 7200 \, \text{s} = 26,821,200 \, \text{J}Energy (J)=3728.5W×7200s=26,821,200J
Step 3: Convert joules to megajoules
1 megajoule (MJ) is equal to 1,000,000 joules. So to convert the energy from joules to megajoules:Energy (MJ)=26,821,200 J1,000,000=26.82 MJ\text{Energy (MJ)} = \frac{26,821,200 \, \text{J}}{1,000,000} = 26.82 \, \text{MJ}Energy (MJ)=1,000,00026,821,200J=26.82MJ
Final Answer:
The 5 hp motor delivers 26.82 MJ of energy in 2 hours.
