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The source of my question can be found via this link:

https://www.youtube.com/watch?v=wwjtuZ5vTvc&index=94&list=PLAD5B880806EBE0A4

There is an object that weight 10N outside of water and 2N inside water. I want to understand the buoyant force acting on it using a free body diagram.

As per the above video, it says that the buoyant force is 8N = 10N - 2N and the free body is drawn as follows

Weight of object 10N downwards and 8N upward buoyant force which gives a net force of 2N. I am confused because if there is a remaining net force of 2N then shouldn't the object be sinking? for it to submerge and not sink the upward force must cancel out the downward force, correct? Can some explain me the forces acting on this object under water? and how to use the weight inside water and outside water to determine buoyant force?

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Yes, you are very correct in saying that if there is a non-zero net force, then the object will accelerate.

  • But consider the first case you mention for example. The object weighs 10 N outside of the water. So, a force of 10 N pulls downwards. Isn't this a net force? So should the object now fall downwards?

No. You must have missed that the object is held up by a scale or a string. The same is the case in the water. Without the string to hold it up, it would sink, because - as you rightfully say - the net force is downwards. But the string gives the remaining force to balance it all.

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The object is suspended from a spring balance end the reading on the spring balance is noted. So in air there is a 10 N force downwards due to the gravitational attraction of the Earth and a 10 N force upwards due to the spring balance so the net force on the object is zero. In water there are three forces: the weight of 10 N downwards, the upthrust of 8 N upwards and a 2 N force upwards due to the spring balance so again the net force on the object is zero.
The 2 N force is sometimes called the apparent weight of the object and can be used to find the density of liquids and solids.

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$F_{net}=F_{buoyant}-F_{weight}$. If $F_{net}>0$, then the object floats, while if $F_{net}<0$, then the object rises up. If $F_{net}=0$, the object remains stationary in the water. Here, the object has a net force of $2N$ acting upwards (as measured by the weighing scale), causing it to stay afloat. Since the object weighs $8N$, the buoyant force can be found to be $10N$.

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