How much energy does a 5hp motor deliver in 2 hours. Answer should be in MJ
The Correct Answer and Explanation is:
To find the energy delivered by a 5 horsepower (hp) motor in 2 hours, we need to follow these steps:
- Convert horsepower to watts:
1 horsepower (hp) is equivalent to 745.7 watts (W). So, a 5 hp motor has a power output of: 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 This means the motor delivers 3728.5 watts of power. - Convert time from hours to seconds:
We need to express the time in seconds, as energy is typically measured in joules, and 1 joule equals 1 watt-second (J = W·s). There are 3600 seconds in one hour, so for 2 hours: 2 hours×3600 seconds/hour=7200 seconds2 \, \text{hours} \times 3600 \, \text{seconds/hour} = 7200 \, \text{seconds}2hours×3600seconds/hour=7200seconds - Calculate the energy delivered in joules:
The formula to calculate energy (in joules) is: E=P×tE = P \times tE=P×t where:- EEE is the energy in joules,
- PPP is the power in watts,
- ttt is the time in seconds.
- Convert joules to megajoules (MJ):
1 megajoule (MJ) is equal to 1,000,000 joules, so we convert the energy to megajoules: 26,853,600 J÷1,000,000=26.85 MJ26,853,600 \, \text{J} \div 1,000,000 = 26.85 \, \text{MJ}26,853,600J÷1,000,000=26.85MJ
Thus, the energy delivered by a 5 hp motor in 2 hours is 26.85 MJ.
Explanation:
Power (in watts) is the rate at which energy is transferred or converted. A 5 hp motor operates at 3728.5 watts, meaning it delivers 3728.5 joules of energy every second. Over 2 hours, this rate of energy delivery results in a total of 26.85 megajoules of energy. The conversion of units from horsepower to watts and from seconds to hours is essential to determine the correct energy output in megajoules. This is a typical approach when calculating energy delivered by motors or electrical devices over time.
