Experiment 1: Fluid Statics

In this lab we measured the buoyant force of the water by using three different methods. We used an underwater weighing method. We also used a displaced fluid method, and we also found the buoyant force by using the volume of the weight.

Underwater Weighing Method

We began by using a force sensor to determine the force of the weight which was 1.099 +/- 0.0005 N.(Picture 1) We then placed the weight in to a graduated cylinder that was filled with water. The force of the weight was lower when it was in the water and it was 0.710 +/- 0.0005 N. Through this method we can determine that the buoyancy force was 0.389 +/- 0.0010 N.

Displaced Fluid Method

We began this method by measuring the weight of the beaker which was 0.217 +/- 0.0005 kg. Next, we had a graduated cylinder filled with water and then inserted our weight slowly. As we did this the displaced water spilled over into our beaker. After the weight was fully inserted we measured the beaker again with the displaced water and it weighed 0.256 +/- 0.0005 kg. By subtracting the two measurements we can determine that the water weighed 0.039 +/- 0.0010 kg. The weight of the water that was displaced is

 0.383 +/- 0.0010 N which is the buoyancy force according to Archimedes' principle. 

Volume of Object Method

We found the volume of the of weight which was in the shape of a cylinder. The volume of a cylinder is 

V = πr^2h so we measured the diameter and the height of the cylinder to determine the volume which was 3.78 * 10^-4 m^3. This would be the volume of water displaced if it were to be inserted into any container with water in it.  The buoyant force of water should be W_f = ρgV where ρ is the density of the water and g is gravity. When using ρ to be 1000kg/m^3 and g to be 9.81 m/s^2 we can determine that the buoyancy force of the water is 0.371 +/- 0.005 N. 

Conclusion

The first method yielded a result of 0.389 +/- 0.0010 N. The second method recorded was 0.383 +/- 0.0010 N. The third method resulted in 0.371 +/- 0.005 N. The first method seems the most accurate because of the experimental method but the uncertainty value is the same as the second method. This was based off of the tools that were used for measurement. The third method has the highest because the tools were the most inaccurate.

I think that the most accurate method is underwater weighing method because the main source of error would be to allow the the weight to touch the ground. If this error is avoided then this method is accurate. The other two methods can have more sources of error by spilling water outside of the beaker or not collecting all of the water that spills because it can spill onto the graduated cylinder. The other method can have error by inaccurate measurements.

If the weight touches the bottom of the graduated cylinder then it incurs a normal force from the surface it is resting on. Therefore, the normal force is now acting on the weight along with the buoyancy force of the water which would lower the value calculated for the buoyancy force.