Buoyant Force

[vivatix]

Can someone explain this one? I am confused.

1. I know that volume submerged = volume displaced so the net volume of the stuff in the container is the same.

2. mass = density x volume
volume is the same, so must only depend on the density of the object (this was my reasoning)

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[nomdeplume1234]

I think this is one of those questions where two answers could be considered correct but one is "more" correct. Even though knowing the density of the object might be helpful, there is a more general answer choice that will for certain be true, which is that there would be weight added to the scale.

 

[Cawolf]

1. I know that volume submerged = volume displaced so the net volume of the stuff in the container is the same.

This is true but not applicable here. Consider that by placing the cube in the water, the water level will rise - intuitively you know that. If the water level rises, there is more "stuff"in the container, and the volume is not the same.

 

[RyanLJ]

This is a purely conceptual problem, and the numbers are only there to trick you into thinking you need them.

Think of it like... you have a cube on a scale, and add a cylinder. Choice B is the equivalent of saying: "The weight of both objects must be greater than the weight of either object alone." The actual weights of the objects are irrelevant to that fact.
In the same way, the question only requires you to recognize that the sum of two forces oriented in the same direction is greater than either one. The initial weight measurement is only the weight of the water+container. The second measurement is the weight of the water+container, and then a force equal in magnitude to the buoyant force exerted by the cube on the water. (Since the buoyant force is oriented upwards, its opposite force is oriented downwards - the same direction as the weight vector.)

You're not usually going to be told when you need to deal with relative comparisons, orders of magnitude, or dimensional analysis to solve a problem instead of calculating the answer, and you may even be deliberately misled into trying to calculate a lengthy problem. Learning to recognize those situations can improve your time.

 

[NextStepTutor_3]

Lots of good answers here! Basically, the previous posters are completely right. Note that the question specifically mentions that only 500 mL of water are initially present in a 1 L container. That leaves a lot of space for the water level to rise once the cube is added. While you were on the right track, adding the cube results in a vessel that now contains 1) the exact same amount of water as before, unless the cube is enormous and causes some overflow and 2) the cube. We've added to the mass of material in the container, so the overall weight should increase. The scale measures the forces that are pointed downward against it and responds with a corresponding upward force.

Also, as a side note, I'm assuming that choice A was the one you found tempting here. In general, watch out for answers that contain words like "must!" While density is certainly necessary for many fluid-related calculations, this is not a quantitative problem. Saying that density "must" be known is therefore an extreme statement.

Good luck