Question

1) What is the power in horsepower of a 100 watt light bulb? What is the power in kilowatts of a 200 horsepower engine?

2) If a cars engine is providing 3000 N of force to keep the car moving at 5 m/s, what is the engine’s effective power?

3) how many gallons of water will be pumped from a well 30 feet deep by a 1/2 hp engine in 1 minute? (1 gallon weighs 8.34 pounds)

Answer 1

1). Use the definition 1 Horsepower = 746 watts

100 watts = (100/746) HP = 0.134 Horsepower

2). Use the definition Power = (work done) / (time to do the work)

and the definition Work = (force) x (distance moved)

(3,000 N x 5 m) / second

= (3,000 x 5 N-m) / second

= (15,000 joules) / second

= 15,000 watts

3). Use the definition Power = (work done) / (time to do the work) , and the definition Work = (force) x (distance moved) , and the 'customary' definition of 1 Horsepower = 550 foot-pounds per second.

Let the answer ... the number of gallons ... be called ' G ' until we know what it actually is.

Weight of water lifted in 1 minute = (G gallons) x (8.34 pounds/gallon)

The distance it's lifted = 30 feet

Work done in 1 minute = (force x distance) = (8.34G x 30) foot-pounds

In just a moment, we're going to need this in seconds:

Power = (8.34G x 30 foot-pounds/minute) x (1 minute / 60 seconds)

Power = (8.34G x 30/60) (foot-pound-minute/minute-sec)

Power = 4.17G foot-pound/sec

The power = 1/2 Horsepower = 225 foot-pounds / sec

So finally, 225 = 4.17G

Divide each side by 4.17, and we have

G = (225/4.17) gallons

G = 53.96 gallons

I really should check this over, but I've had it up to here with gallons, feet, horsepower, and pounds, so I'm not gonna do it. Read my lips. It is what it is. I stand or fall by my answer. What could go wrong ? !