Fluid Statics Laboratory

Re-purposing a digital force sensor as a scale is pretty efficient.

This picture shows a Vernier force sensor, attached to a laptop which is running logger pro. An aluminum cylinder is connected to the force sensor by a string.
The cylinder was measured to weigh .229 ± .006 Newtons when suspended in air.
When suspended in water, it was measured to weigh .165± .006 Newtons.
The difference between these two measurements is the buoyant force on the cylinder due to the volume of water it displaces.
The buoyant force was determined to be .064±.012 Newtons.

Another Method for determining the buoyant force is to submerge the cylinder in a vessel which is nearly overflowing. The action of submerging the cylinder will displace a volume of water from the overflowing vessel, and the weight of the overflow is equal to the buoyant force.

We achieved this measurement by placing a large beaker on an electronic scale. We then zeroed the scale with the beaker on it. We then placed a cup nearly filled with water into the beaker and submerged the cylinder.

The first attempt did not result in any overflow, due to the surface tension of the water.

On the second attempt, we filled the cup until the surface tension brought the water line above the edge. Once the cylinder was submerged, an amount of water flowed into the larger beaker. we then removed the cup and cylinder from the beaker and used the scale to measure the mass of the water in the beaker.

The mass displaced was recorded as 6.8 grams and this translates to a weight of .0666 ±.005 Newtons.

This differs from our first measurement by approximately 4± 4%

The final method for determining the buoyant force was to measure the volume of the cylinder using vernier callipers.

Our cylinder's diameter was recorded to be .0143 ± .0001 meters, the height was recorded to be .0484 ± .0001 meters. By the formula for the volume of a cylinder:

Our Volume was determined to be approximately:
7.77±.01 *10^-6 meters cubed.

the density of Deionised water at 23 degrees Celsius, (the temperature of the laboratory at the time of the experiment) is approximately 997.568 kg/m^3.
This results in a mass of displaced water approximately:
.00775442 kg

The weight of that water would be .0761±.0001 Newtons.

That is a 16±1% increase over the reading from the force sensor and a 14±1% increase over the prediction from the scale test.

Despite this calculation's significant deviation from the previous two values, it is in all likelihood the most accurate. The scale and force sensor may not have been properly calibrated, and the experimental procedure was rushed. On the scale trial, there may have been some water still adhering to the cup as it was withdrawn from the beaker. The force sensor was only casually calibrated, and may not have high enough resolution for the scale of the measurements we were taking.

The vernier callipers are at least high enough quality that we can be confident about the measurements up to the hundredth of a centimeter, this represents less than one percent uncertainty in that measurement.


-B