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 roll the ball in order to make it to the other side, say 10 metres total distance.
*Assume zero friction and assume the ball doesn't slow down or speed up after you've released it.
At least the horizontal velocity should help the ball to finally touch ground or water after falling through the bridge a bit further by increasing the speed. The only other hope is that the bridge needs time to collapse, and you would shorten the time the bridge has to do this. But really, if the bridge is long enough, and horizontal, any force that you apply on the ball horizontally (in the direction of the other side) will not affect the gravitational force, which is orthagonal to the bridge.
Horizontal motion does not oppose or counter downward forces, but the good news is that it does not add to it either.
My answer to your question is therefore that your premise of roll it fast enough is flawed.
There is, however, perhaps a small caveat to this. The collapse of the bridge takes time. It may also be the case that only the section where the ball is experiences the overly powerful downward pull of gravity on the ball.
You *might* be able to get the ball across if it moves fast enough that the collapse does not have time to occur, even though I suspect the bridge might still suffer damage from the short time it experienced the overburden.
This is my analysis of the problem.
Originally posted by geepamoogleYou are starting to catch on.
Horizontal motion does not oppose or counter downward forces, but the good news is that it does not add to it either.
My answer to your question is therefore that your premise of roll it fast enough is flawed.
There is, however, perhaps a small caveat to this. The collapse of the bridge takes time. It may also be the case that only the section ...[text shortened]... damage from the short time it experienced the overburden.
This is my analysis of the problem.
The entire bridge will not collapse at the same moment. Only the section of the bridge that the ball is/was on will collapse. By the time the section of the bridge collapses, if the ball is moving fast enough the ball may already be on to the next section of the bridge.
In other words, is it possible for the ball to travel along the bridge and have the bridge collapse bit by bit as the ball moves? Or will the ball just immediately crash through the first section of the bridge regardless of the speed at which it is travelling?
It's like when you drop into the water from a waterslide. You'll slide on the water for a couple meters. So even though you can't be supported by the water really you don't go down directly. The metaphore is not 100% but you get what i mean.
Unfortunately i think that you'd have to give some info on the bridge and what materials and composition it is in order to be able to calc a definite answer.
Also the bridge has 2 solid points where the ball would be supported and thus you need to consider if the ball breaks at the edge then it would break it even 'harder' at the middle. And so on. Not easy to calculate imo but not at all impossible if you make some generalizations.
My thoughts 🙂
Originally posted by TeraWater's a little different because it has surface tension.
It's like when you drop into the water from a waterslide. You'll slide on the water for a couple meters. So even though you can't be supported by the water really you don't go down directly. The metaphore is not 100% but you get what i mean.
Unfortunately i think that you'd have to give some info on the bridge and what materials and composition it is in orde ...[text shortened]... lculate imo but not at all impossible if you make some generalizations.
My thoughts 🙂
Originally posted by uzlessIf it rolled at the speed of light (or very close to it), wouldn't it start to
What if you rolled the ball at the speed of light?
What do you think would happen to the bridge?
have increasing mass? Wouldn't that make its weight greater, making
the effect of gravity more significant?
Nemesio