# Help with simple problem

1. Aug 30, 2004

### Juntao

help with simple problem:(

An electric wheelchair is powered by two 12 V lead acid batteries and an electric motor rated at a maximum output power of 1 hp. Each battery has an energy capacity of 600 W-hrs. The motor has an efficiency rating of 89%. Assuming that the batteries are fully charged, for how many minutes can the motor deliver the rated output power before the batteries must be recharged?

Ok, this seems such an easy problem, but I cant get it to work just yet.

I know that P= V*I
and Energy = P_avg*Time
1 hp = 746watts

Ok, so I have two batteries, each battery has capacity of 600 W-hrs, so total I have 1200 W-hrs.

In the end, I want to be able to take the 1200 W-hrs, divide by some number of watts to get hrs, then convert hrs to mins.

But I do not know how to use the 89%. I thought maybe I have to use the hp conversion factor, so I tried doing this, 1200 W-hrs/(746W*.89)*(60min/1hr) but that didn't work. Can somebody lead me in right direction?

2. Aug 30, 2004

### chroot

Staff Emeritus
The motor is 89% efficient. It takes in more power than it puts out, and converts the rest to heat. What power must it take in that when multiplied by 0.89 is 1 hp?

1 hp / 0.89 = 1.12 hp.

The motor must take in 1.12 hp, 89% of which is converted into 1 hp of output power.

Now convert 1.12 hp into watts:

1.12 hp * (746 W / 1 hp) = 838 W

How many hours will the 1200 W-hr battery pack run the motor?

(838 W * ? hr) = 1200 W-hr

The result is just a division. 838 W for how many hours is the same total energy as 1200 W for 1 hour?

- Warren

3. Aug 30, 2004

### Juntao

awesome

thank you so much...you are a true godsend.