Fluid Statics Lab

Lab Objective

Experimentally verify the theoretical effects of the bouyant force on an object submerged in water.

Lab Equipment

-Lab Pro set up with Force Probe

-String

-Overflow can

-Beaker

-Metal cyinder with hooks

-Meter stick

-Vernier Calliper

Lab Procedure (data collection)

1) use a force probe to measure the weight of a metal cylinder suspended in the air.

2) suspend the metal cylinder in the overflow can and measure the new reading on the force probe as well as the amount of water that spills out of the overflow can

3) measure the dimensions of the metal cylinder

Collected Data

Force Probe reading- 1.099N in air, 0.710N in water (error = 0.001N)

Mass of water spilled from overflow can- 0.0387kg (error = 0.005kg)

Mass of metal cylinder- 0.112kg (error = 0.001kg)

Diameter of metal cylinder- 0.025m (error = 0.01m)

Height of metal cylinder- 0.077m (error = 0.01m)

Calculations and Analysis

In order to find the experimental value of the bouyant force we find the difference between the two force probe readings.

Fb = Fa - Fw

Our measured value for the bouyant force lies between 0.387N and 0.391N

Next we compare this value to the weight of displaced water, assuming g = 9.81 m/s^2

Fb = W = g(Mw)

The measured weight of displaced water lies between 0.374N and 0.384N

These two values are close but the intervals do not overlap. This was most likely caused by water sticking to the overflow can as it spilled out. This would result in the measured weight of displaced water to be less than the actual bouyant force.

We also compared these bouyant force values to the theoretical weight of displaced water found by measuring the volume of the metal cylinder and multiplying by the density of water and acceleration due to gravity, assuming rho = 1000kg/m^3, g = 9.81 m/s^2

Fb = W = V(rho)(g) = pi(d/2)^2(h)(rho)(g)

This value for the bouyant force lies between 0.337N and 0.406N

This interval agrees with both previous intervals but is much wider due to the propagation of errors in measuring the dimensions of the cylinder.

Summary

1) Compare the 3 values for the bouyant force
The 3 intervals we obtained for the bouyant force (3.87-3.91, 3.74-3.84, 3.37-4.06) seem to agree with eachother fairly well. The intervals were constructed by calculating the lowest and highest possible values of the bouyant force given the initial measurements and errors. The first and second intervals did not overlap, but this was probably due to water residue from the overflow attaching to the overflow can.

2) Which method do you think was most accurate and why?
I think that the most accurate method for obtaining the bouyant force was by using the force probe because it measured the force more directly than the other methods and there was little room for experimental errors when simply using a force probe to measure a force. Also, the interval constructed from the force probe measurements was significantly smaller than the other two intervals.

3) If the cylinder had been touching the bottom of the water container, how would that have changed your value for the bouyant force?
If the cylinder had been touching the bottom our measurement for the bouyat force would have been much higher than the actual value. This would have been due to the normal force between the cylinder and container which would act upward on the cylinder and cause the measuerements of the force probe to be significantly lower.