I was reading about the San Francisco Forty-NIners ground-breaking ceremony for the new stadium in Santa Clara. An article from the Sacramento Bee’s 49ers blog discussed the measures taken in contstruction and design to make it more environmentally friendly and energy efficient.
One of the signature features will be a living green roof, which is supposed to help the building itself use less energy. Here’s the physics problem:
“One of the problems Jack Hill, the project executive for the 49ers’ new $1.2 billion stadium, currently is facing is how to transport 2,000 tons of dirt and top soil 150 feet in the air.”
So how much energy is required to transport that mass of soil up 150 ft? Is it even possible that the building’s energy usage would be reduced enough by the green roof to ofset the energy cost of the roof’s construction?
Naturally, I’ll answer the first question in metric units:
1.8 x 10^6 kg * 9.8 m/s/s * 46 m = 8.1 x 10^8 J = 225 kWh
So what? Looks like I have reason to contact some Environmental Science students and see what they make of this, either that or pay more attention to my home energy bill. The 225 number doesn’t seem that huge, so eventhough it may be difficult and time consuming to get the soil on the roof, in a back-of-the-envelop conservation-of-mechanical-energy sort of way its not too much trouble to get the soil up there.