Question

How much energy does a 10-hp electrical motor deliver in 40 minutes? Assume that 1 horsepower (hp) = 746 W. Provide your answer in Joule (J) and kWh.

Answer 1

We are given that a 10hp electrical motor will deliver an amount of energy for 40 minutes. To determine the amount of energy we will use the fact that electric power is defined as the energy divided by time. Its formula is:

`P=(E)/(t)`

Now we solve for the energy by multiplying both sides by time:

`Pt=E`

Now we plug in the values:

`(10hp)(40\min )=E`

Solving the operation:

`400hp\min =E`

Now we convert hp into W using the provided conversion factor and we will convert min into seconds for our answer to be given in Joules. The conversion factor for minutes into Seconds is:

`1\min =60s`

Using the conversion factor we get:

`400hp\min *(746W)/(1hp)*(60s)/(1\min )=17904000J`

Now we will convert the quantity into kWh first by converting the hp into kW using the following conversion factor:

`1hp=0.746kW`

And we will convert minutes into hours using the following conversion factor:

`1\text{hour}=60\min`

Converting the quantity we get:

`400hp\min *(0.746kW)/(1hp)*(1h)/(60\min )=4.97kWh`

Therefore, the total energy is 17904000 Joule or 4.97 kWh.