Fluid Statics Lab

The purpose of this lab is to measure the buoyant force on an object with different methods , and we are going to determine which way is the most effective way to find the most accurate buoyant force. We are going to use underwater weighing method, displaced fluid method and volume of object method to find the buoyant force.

Firstly, we use underwater weighing method to find buoyant force. To find the buoyant force, we consider the forces acting on a metal cylinder. We assume there is no frictional force. We have the buoyant force.

Buoyant force B = W - T

where W is the weight of metal and T is the tension of string on metal. We find the weight of the metal cylinder in air by putting the metal on a electrical scales to find the mass

The mass of metal = 0.2655 kg ± 0.00005 kg
The weight W = mg

We find the weight of metal in water is equal to itself in air as we think the weight is only dependent of the gravity.

Buoyant force B = mg - T

We use the force probe to measure the tension T.

Tension T = 0.927 N ± 0.05 N

We have the buoyant force B calculated.

The uncertainty of buoyant force B = ((9.81 ms^-2)^2 x (0.00005 kg)^2 + (0.05 N)^2)^1/2 = 0.0500 N

Buoyant force B = (0.2655 kg)(9.81 ms^-2) - 0.927 N = 1.678 N ± 0.050 N

Secondly, we use displaced fluid method to find buoyant force. To find the buoyant force, we measure the weight of water displaced by the metal. We put the dry plastic cup on electric scales to measure the mass of cup.

Mass of cup = 0.0104 kg ± 0.00005 kg

We put the beaker fully filled with water at the edge of table. We put the metal into the beaker and use the dry cup to catch the excess water dripping from overflow. We use the electric scales to measure the mass of cup with excess water.

Mass of cup with excess water= 0.0351 kg ± 0.00005 kg

The weight of excess water = (0.0351 kg - 0.0104 kg(9.81 ms^-2)= 0.242 kg ± 0.0005 N
According to Archimede's Principle, we have the buoyant force B equals to the weight of excess water
The uncertainty of buoyant force B = (9.81 ms^-2)(0.00005 kg)= 0.0005 N
Buoyant force B = (0.0247 kg)( 9.81 ms^-2) = 0.242 N ± 0.0005 N

Thirdly, we use volume of object method to find buoyant force. To find the buoyant force, we
have to know the volume of displaced water in cylinder.

The volume of displaced water in cylinder V = (pi)(r)^2(h) = (pi)(D/2)^2(h)

where r is the radius, D is the diameter, and h is the height of cylinder.

Height of cylinder measured h = 0.05 m ± 0.005 m
Diameter of cylinder measured D = 0.016 m ± 0.0005 m

The density of water = 1000 kgm^-3
The uncertainty of displaced water = (((pi)(1000 kgm^-3)(2)(0.016 m)(0.05 m)(9.81 ms^-3)(0.0005))/4)^2 + (((pi)(1000 kgm^-3)(9.81 ms^-3)(0.016 m)^2(0.005))/4)^2)^1/2 = 0.0116 N
The Weight of displaced water = The Buoyant force B = 1000Vg = (1000 kgm^-3)(pi)(0.016 m/2)^2(0.05 m)(9.81 ms^-3) = 0.099 N ± 0.0116 N

Summary/ Conclusion:
After conducting this fluid statics lab, we find the buoyant force, and we have the conclusion that the underwater weighing method is the most accurate method the determine the buoyant force of an object in the water according the experimental data and error of three methods in this lab mentioned in the following.

1. Values for the buoyant force:
A : Underwater weighing method : 1.678 N ± 0.0500 N
B : Displaced fluid method : 0.242 N ± 0.0005 N
C : Volume of object method : 0.099 N ± 0.0116 N

2. I think the underwater weighing method is the most accurate method to find buoyant force.
In the displaced fluid method, we cannot catch all the excess water very well as we let some of the excess dripping from beaker outside the dry cup, and the missing water should be taken account for measuring the displaced water as the missing water is part of the displaced water, which makes the water displaced in experiment significantly lower than in expected. It makes the mass, weight of water displaced and Buoyant force in experiment significantly lower than in expected. As we loss part of water in the displaced fluid method, the buoyant force found in the volume of object method is less accurate. It is because the water measured in displaced fluid method is not accurate, and there is some water remain in the cup when the water is transferred into the cylinder. We loss more water in this method than in displaced fluid method. The volume of water displaced in cylinder is much less than expected. Even we have accurate value of density of water, we cannot find the weight of water accurate because of the great loss of displaced water. Even the uncertainties of the buoyant force in underwater weighing method is greater than the uncertainties for the other two methods. However, the value of uncertainty is very small compared to the error result from losing the water from the beaker in displaced fluid method as we miss almost 1/3 of water from beaker, which makes the buoyant force in displaced fluid method and volume of object method decreases significantly. As a result, I think the underwater weighing method is the most accurate method to find buoyant force.

3. If the cylinder is touching the bottom of water container in underwater weight method. The value for the buoyant force would be lower than the value for buoyant force without touching the bottom. It is because there is upward normal force N acting on the container.

Buoyant force B = W - T - N

There is also normal force N that is opposite to buoyant B, so the buoyant force B becomes smaller.