Cat Horsepower

Saturday, April 25, 2009

My cat, Jupiter, crouches on the carpet below the window, then leaps up onto the window-ledge, a leap of thirty-nine inches.

Jupiter is overcoming gravity; that is, he is reversing what would happen were he, or a marble, to roll or fall off the window ledge onto the floor.

I know that acceleration due to earth’s gravity is 32 feet per second per second.

I know that Newton’s formula for distance is

S= ½ a t^2

Since I know the distance (39 inches or 3.25 feet) and I know the acceleration (32 feet per second per second), I can work out the time it would take him, at most, to fall from the ledge, and hence the time taken, at most, to leap onto the ledge.

0.45 seconds. Roughly (!)

Now Jupiter weighs thirteen pounds, roughly. I know this because I picked him up yesterday and stood on the scales with him. Then I put him back in the green chair and weighed myself.

So when Jupiter leaps up to the window ledge, he is lifting 13 lbs through a distance of 3.25 feet. In other words, he is doing 13x3.25=42.25 foot-pounds of work.

And he does it in 0.45 seconds.

It’s not a truly fair translation, but roughly speaking, he could lift 93 foot pounds in a second, could he maintain his rate of work. Which he probably couldn’t.

Since a crude definition of “One Horsepower” is 550 foot-pounds per second, and Jupiter can manage 93 foot-pounds per second, I conclude that my cat Jupiter is rated at about 0.17 of a horsepower!

Or, if you prefer, 5.8 cats like Jupiter would be as good as having a horse.

He doesn’t eat like a horse, though.

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