Saturday, March 19, 2011
I love this video.
But since I've been harping on weight and mass lately I think I'll take some time to brush up on my high school physics. At around 4:13 in the video James says the lunar rover has two stated weights. Approximately 4 tonnes on earth or 760 kilograms on the moon. I'm pretty sure he meant tonnes, 1000 kilograms, not tons, 2000 pounds.
But what did he mean about it performing differently? Well, real weight is a force vector. Force = mass times acceleration, this time acceleration is gravity, 9.8 meters per second per second on the earth, or 1.63 m/s^2 on the moon. Weight has direction. The lunar rover on the earth exerts a downward force of
F(earth) = 4000 kg x 9.8 m/s^2 = 39,200 kg m/s^2
F(moon) = 4000 kg x 1.63 m/s^2 = 6,520 kg m/s^2
A kilogram meter per second squared is a newton, the proper SI unit for weight. People say weight when they mean mass just like they say motor when they mean engine. It's not right, but to correct them would be rude. Context usually makes it clear what they meant. When he says 760 kilograms he means something that weighs 760 kilograms on earth would press down as hard on the earth as the lunar rover presses down on the moon. So picture a Smart car on the Earth and the lunar rover on the moon -- same force vector down towards the ground. Good thing the rover has so many more wheels because it will need the extra surface area to provide necessary traction.
Inertia is the thing that has the same units as weight. It's the mass times the acceleration again, but this time not the gravitational acceleration but the actual acceleration from the torque in those wheels moving the rover forward, or sideways, or whichever direction it wants to go.
Inertia isn't what we have values for though, so let's just look at the momentum. If the rover is going along at 10 miles an hour (top speed at 2:45 in the video) or about 4.5 m/s to keep our units consistent*, it has the same momentum on the moon as on earth.
p(rover) = 4000 kg x 4.5 m/s = 18,000 kg m/s
p(Smart) = 760 kg x 4.5 m/s = 3,420 kg m/s
There's no shorthand unit for momentum, or good explanation for why the symbol is p. This would be a vector going straight ahead. So the Smart car would have a lot less momentum than the Rover.
I've never driven a Smart car though so I don't know what that's like. The rover is about 3 times more massive than my Honda station wagon. If I move that multiplier to the speed instead of the mass it would be like my Honda station wagon going 30 miles per hour but with the traction of that cut-down VW bug we had when I was a kid. I'm kind of terrified just thinking what it would be like to drive that. I guess the good news is that on the moon you don't have trees to hit when you swerve to miss a tortoise. Slamming on brakes would be out of the question in that scenario; you'd never stop in time.
I bet the dynamics of the tipping would be all different. A low center of gravity would be a lot less important on the moon. Yes, I'm agreeing that he chose a good word. The performance would be "different."
I want to go and perform some traction and inertia experiments in the field on my mountain bike now though. I have thought about this enough now to remember why I don't design vehicles for a living.
*If you don't know about the Google unit converter or calculator you should. You just type in the search window "10 mph in m/s" hit enter and get the answer