Archimedes' Conceptual

[MedPR]

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Still having problems with this concept. I found a ppt from mit.edu and would like some help with the questions (they don't provide answers).

Imagine holding two bricks under water. Brick A is just beneath the surface of the water, whilebrick B is at a greater depth. The force neededto hold brick B in place is
A.larger
B.the same as
C.smaller
than the force required to hold brick A in place.

Assuming the bricks are the same mass, the answer to this question would be A, correct? Since B is deeper it has a greater force acting on it due to the larger column of water above it compared to brick A?

A 200-ton ship enters the lock of a canal. Thefit between the sides of the lock and the ship istight so that the weight of the water left in thelock after it closes is much less than 200 tons. Can the ship still float if the quantity of waterleft in the lock is much less than the ship'sweight?
A. Yes, as long as the water gets up to the ship'swaterline.
B. No, the ship touches bottom because it weighsmore than the water in the lock.

B? If mg=density*volume*gravity, then the mass of the water must equal the mass of the object, and since it says the water is less than 200tons, it is less than the ship. So the ship will sink..?

When a hole is made in the side of a container holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow
A. diminishes.
B. stops altogether.
C. goes out in a straight line.
D. curves upward.

This one isn't really archimedes', but I couldn't figure it out for sure either.

Is it C?

 

[chiddler]

my humble attempt:

1. Is C because brick 2 is submerged and the buoyant force is greater. Depth only changes pressure.

2. B. Weight displaced is equal to weight of object. Not enough to displace? cannot float.

3. Free body diagram. Water spurting out starts out with linear lateral momentum. Then it starts dropping due to gravity. In freefall, gravity doesn't take effect so i think it'll be a straight line to the side.

 

[milski]

Q1: B

The only forces acting on the bricks are gravity and buoyant force. If they're both fully submerged, have same mass and same volume, the net force will be the same. In detail: same mass -> same weight. Same volume in the same fluid -> save buoyant force. Same weight + same buoyancy -> same net force.

You are correct that the one that's deeper will have larger force pushing it down but it will also have larger force pushing it up. The difference between the two is known as buoyant force and does not depend on depth.

Q2: A

The ship has to weight as much as the water displaced. That is, as much as the water that would fit in the hole made by the ship. Since the level of the water can go up as necessary, the displaced amount can be as much as needed.

Another way to think about this one: the ship will float in a huge tank. Now make the tank twice as small. Does anything change? No. You can keep making it smaller and smaller until you have it tightly fitting the shape of the ship and the ship would not feel it. There is a minimum "thickness" of the water layer at which you'll start having problems but that's more complicated matter which is not related to basic buoyancy.

One more thought on this one: the mass is not of the water around the ship but the water which could occupy the space where the ship is.

Q3: Yes, it's C.

The water flows because of pressure differences between the top and the bottom of the container. They'll still be there even when the container is falling. The vertical component of the motion will be the same for water particles inside and outside of the container (ignoring air resistance), so the flow will be horizontal.

 

[chiddler]

just for my pride:

1. i meant B!

thanks for the good #2 explanation.

 

[milski]

just for my pride:

1. i meant B!

Third time is a charm. 😉

 

[chiddler]

hahaha bad luck >.>