Weight of barge on a bridge canal/acqueduct

[bigboss]

Homework Statement

In England in the Middle Ages an extensive system of canals was used for transportation. Some of these canals crossed over canyons by flowing over bridges (viaducts). Suppose that a heavily loaded barge crossed over such a waterway bridge.

A)The force on the bridge would not change when the barge passed over.

B)The force on the barge would become less because some water would be squeezed off of the bridge.

C)The force downward on the bridge would increase because of the added weight of the barge.

D)The force on the bridge would become less because of the buoyancy effect of the water on the barge.

E)Whether or not the force on the bridge would increase or decrease would depend on whether the water was flowing or stationary.

Homework Equations

Fb= mg=pvg

The Attempt at a Solution

i believe it is C, but i am not very sure

 

[Astronuc]

The barge displaces an equal mass of water, i.e. the mass does not change.

 

[mgb_phys]

In England in the Middle Ages an extensive system of canals was used for transportation.

The 18century is middle ages?

 

[bigboss]

so if the mass does not change, what does that mean?

 

[cepheid]

The barge displaces an equal mass of water, i.e. the mass does not change.

"Displaces" doesn't necessarily mean, "causes to spill out of the aqueduct," does it? What if there is more than enough extra room?

Also, doesn't the barge displace an equal volume (not mass) of water i.e. equal to the volume of the portion of the barge that is submerged?

 

[Phrak]

Does the bow wave add mass?

 

[ideasrule]

""Displaces" doesn't necessarily mean, "causes to spill out of the aqueduct," does it? What if there is more than enough extra room?"

Because of choice B (...because some water would be squeezed off of the bridge), I think the question assumes there's no extra room. That's ridiculously unrealistic, of course, but so are most physics problems.

"Also, doesn't the barge displace an equal volume (not mass) of water i.e. equal to the volume of the portion of the barge that is submerged?"

Both are true. If the barge is floating, it displaces a volume of water equal to the volume of part of the object that's submerged, but if that volume is filled with water, its weight would equal that of the barge. If this weren't the case, gravity and buoyancy wouldn't balance, and the barge would move upwards or downwards until they do.

 

[bigboss]

i am still not understanding this, what would be the answer?

 

[Phrak]

The Falkirk Wheel in Scotland for extra credit.

http://cache.gizmodo.com/gadgets/images/falkirk_wheel.jpg

 

[cepheid]

Both are true. If the barge is floating, it displaces a volume of water equal to the volume of part of the object that's submerged, but if that volume is filled with water, its weight would equal that of the barge. If this weren't the case, gravity and buoyancy wouldn't balance, and the barge would move upwards or downwards until they do.

Right. I knew that.

I think this is a badly worded problem though. If we're supposed to make certain assumptions when answering it, then that should be stated explicitly.

i am still not understanding this, what would be the answer?

Initially the aqueduct contains a certain mass of water which has a certain weight. This weight is supported by the bridge.

If we go with Astronuc on this one, then after the barge starts traversing the aqueduct, the total mass of stuff in the aqueduct (water + barge) DOESN'T change compared to what it was initially. If the total mass of stuff in the aqueduct is the same, then what about its weight compared to before?

 

[bigboss]

then the weight would be the same

 

[Astronuc]

then the weight would be the same

mass doesn't change therefore weight doesn't change.

 

[Astronuc]

The Falkirk Wheel in Scotland for extra credit.

http://cache.gizmodo.com/gadgets/images/falkirk_wheel.jpg

[/URL] That's very cool.

 

[bigboss]

mass doesn't change therefore weight doesn't change.

therefore, force does not change? A?

 

[ideasrule]

"therefore, force does not change? A? "

With the assumption that any water the barge displaces spills out of the aqueduct, yes.

 

[rl.bhat]

When there is no barge on the canal, the weight on the bridge is the weight of the water in the canal. When the barge enters the canal, buoyancy act on the barge, which is equal to the loss weight of the barge. Equal and opposite reaction of the barge act on the bridge through water. So the choice is C.

 

[LowlyPion]

When there is no barge on the canal, the weight on the bridge is the weight of the water in the canal. When the barge enters the canal, buoyancy act on the barge, which is equal to the loss weight of the barge. Equal and opposite reaction of the barge act on the bridge through water. So the choice is C.

If the presumption is that the water level is invariant, because the barge is already in the water before entering the water bridge, as well as after, then the mass borne by the bridge looks also to be invariant, (as Astronuc, ideasrule, et al have pointed out). The buoyancy that supports the boat, the displaced water, accounts for the whole weight of the boat. So yes the barge bears down on the water and the water on the bridge, but there is less water bearing down on the bridge that nature has conveniently managed to make identical to the weight of the barge in floating it in the first place.

I'd say where any additional weight is added is at the point that the boat initially enters the bodies of water on either side of the bridge, and the water level minutely adjusts itself over all the water from that point onward.

 

[Phrak]

"therefore, force does not change? A? "

With the assumption that any water the barge displaces spills out of the aqueduct, yes.

no, no. The extra water can go anywhere. It can spill out of the canal, or the presence of the boat forces the water up and down the canal, as long as the level of the water is the same.

And Yes, the force doesn't change. Weight is a force.