# Buoyancy Formula (Fb, mdg, T etc)

## Homework Statement

Hi Everyone! I'm new to this forum and a beginner at physics so I hope to get some help! :-)

I am doing a report for a lab we did a few weeks ago, and it happens to be one where I was feeling awful and obviously not paying enough attention!

We were using a rubber duck with a weight, submurging it in water and measuring the mass and volume of the duck and then finding its mean density.

The mass of the duck = 70g
The mass of the weight used = 30g

One of the questions asks:

"Write an equation relating the buoyant force B, gravitational force mdg on ducky, the tension downward due to the small force of weight W and the tension T upward provided by the string and spring balance. Use this equation and the measurements of T and W and ducky's mass md to deduce the buoyand force and hence the volume of water displaced"

## The Attempt at a Solution

Now, I have an equation at the bottom of my page that says the volume of the water is 1x10-4L and the density of the duck is (0.07)(1.10-4) = 700 kgl-3

And another that says the weight of the duck is .686N.

Do these sound correct? And what would be the equation they are asking for above?

Maybe I shouldn't do these assignments so late at night, but I feel at bit lost! lol

## Answers and Replies

So you're measuring the weight of the ducky underwater? Draw yourself a free body diagram. Then use Newton's second law to derive an equation for the forces on the ducky acting in the vertical direction.

Once we have the equation we have to use the T, Md and W measurements to find the bouyant force and volume of water displaced.

My eqution is Fb = Mdg

Does the tension force upward and the 30g weight downward cancel out?

I have the mass as 0.07kg and volume of water displaced 1x10-4; and the buoyoant force as .686N

I'm assuming the weight was used to make ducky fully submerge.

Forget the water for a minute, just suspend ducky from the scale and look at the fbd. The magnitude of T should be equal and opposite to the weight of ducky plus the extra 30gm weight, right, that is, whatever is registering on the scale? Now add water. The new weight measured is the actual weight minus the buoyancy force. The buoyancy force is also equal to the weight of the water displaced. I am guessing that is 1e-4m^3 (cubic meters) or 100 cubic centimeters of water. what is the weight of this much water?

in the end: density=mass/volume =70g/100cc= 0.7g/cc which can be converted to units of kg/l be first dividing by 1000 to convert g to kg and multiplying by 1000cc/L, which cancel out. (a m^3=1000L)

Since it is less than the density of water, this is why the additional mass was used, otherwise Mr Ducky would have been floating.