Experiment 1: Fluid Statics

The purpose of this lab is to measure the buoyant force acting on a cylindrical metal using three different ways: (A) underwater weighing method, (B) displaced fluid method, and (C) volume of object method.

Part A: Underwater Weighing Method

The forces experienced by the metal cylinder when it is submerged in the water are shown in the free-body diagram below:

Free-Body Diagram

From the free-body diagram, we can conclude that buoyant force can be expressed as:

B = mg – T

where mg is the weight of the cylinder in air and T is the weight of the cylinder in water.

The weight in air and in water can be measured using a force sensor.

Measuring the weight of cylinder in water

Measuring the weight of cylinder in air

mg = 1.09 ± 0.05 N

T = 0.70 ± 0.05 N

Hence, B = 0.39 ± 0.10 N

Part B: Displaced Fluid Method

                In this part, according to Archimedes’s principle, we can measure the buoyant force experienced by the cylinder by calculating the weight of the water that is displaced.

Mass of beaker = 0.141 ± 0.0005 kg

Displacing water to calculate the mass of displaced water

Mass of beaker and displaced water = 0.180 ± 0.0005 kg

Mass of displaced water = Mass of beaker and displaced water – Mass of empty beaker

                                      = 0.039 ± 0.001 kg

The weight of displaced water is then given as:

W_f = (Mass of displaced water) * g = 0.383 ± 0.009 N

According to Archimedes’s principle, the weight of displaced water is equal to the buoyant force experienced by the cylinder, therefore:

B = 0.383 ± 0.009 N

Part C: Volume of Object Method

                In this part, as in part B, we use the Archimedes’s principle to find the buoyant force experienced by the cylinder.

Measuring dimension of cylinder using a caliper

r = 0.0125 ± 0.0005 m

h = 0.077 ± 0.0005 m

Volume of a cylinder can be found using the formula: V = πr²h

V = 3.78 x 10^-5 ± 0.327 x 10^-5  m³

The weight of displaced water can be solved from the formula:

W_f = mg = ρVg

Using ρ = 1000kg/m₃ :

W_f = B = 0.371 ± 0.0321 N

Table of Results

	A	B	C
Buoyant Force	0.39 ± 0.10 N	0.383 ± 0.009 N	0.371 ± 0.0321 N

Questions
1.       Based on the table of results shown above, the three values seem to fall within the same range. Uncertainty values are approximated from the tools and techniques used in this lab, and calculations are shown below:

2.       Based on the value of uncertainty, the second method, displacement method, seems to be the most precise. We only used the balance in this portion of the lab, which is more accurate compared to the force sensor and caliper. The displacement method also doesn’t leave much room for error.

3.       If the metal cylinder had been touching the bottom of the beaker in the first part, the buoyant force would have been too low. The cylinder would experience a normal force pointing upward caused by the beaker, therefore smaller buoyant force is needed to balance out the weight of the cylinder.