Originally posted by uzless
I have a 10 pound ball. I have to get it across a bridge but the bridge can only support 5 pounds of weight.
My solution is to roll the ball across the bridge so that the horizontal momentum of the ball will decrease the vertical pull of gravity enough so that the ball will make it all the way across the bridge.
What is the minimum speed that i have to ...[text shortened]... sume zero friction and assume the ball doesn't slow down or speed up after you've released it.
Okay, now I've read the question again. I agree that you're not asking about the fastest speed, but the minimum speed of the 10 pund ball.
I think we have not got all the neccesary facts obout the bridge. You haven't said anything about if the bridge is flat or not. I assume therefore tha bridge is flat. Also that the bridge is long enough to make this qeustion interesting. 1 cm long bridge is not interesting.
How much is 10 pounds of weight? Is is about 5 kilograms, or am I far way out? If we're talking about 5 kg, do we really need a bridge? Never mind, the bridge perhaps is made of spagetti, it doesn't really matters.
In the real world, if the builder says that the bridge can support 5 pound, he says that he garantuee this, not that it will collapse with even the slightest weight over 5 pounds. Under a short period of time it will support for perhaps 10 pounds, perhaps not. We need to know what the builder says about this. But since you don't mention any garantuees, we can assume that 5.0001 pounds will brake the bridge into pieces.
So, assuming that the bridge is flat, and will collaps if it is stressed more than 5 pounds, I don't think there is no lower nor upper limit in velocity. It will break anyway.
Edit: Now I have read the enire thread. Some has the same ideas that I have, others not. But I still think that vital information is missing. There is no way to calculate the minimal velocity if you don't assume things by yourselves. I still say the bridge will collaps.