Experiment 1: Fluid Statics

Purpose: 
To experimentally measure the buoyant force acting on an object.  This will be done three different ways and then compared. 

Equipment: 

• Force Probe
• String
• Beaker
• Flask
• Caliper
• Cylinder to be tested

Experiment:

A)  Underwater Weighing Method

 

With the force sensor in the vertical position, a string connects the cylinder to the sensor.  Logger Pro will measure the tension in the string due to the cylinder.  Measuements will be taken with the cylinder in air and in water (as shown above).  The buoyant force is the weight minus the tension. 

 

Below are the measurements taken from Logger Pro. 

Trial	Sensor Readings
	Air	Water
1	1.140 ± .01 N	0.769 ± .01 N
2	1.148 ± .01 N	0.759 ± .01 N
3	1.138 ± .01 N	0.763 ± .01 N
Avg	1.142 ± .01 N	0.764 ± .01 N
Min	1.132 N	0.754 N
Max	1.152 N	0.774 N

The minimum buoyant force is:

1.132 N - 0.774 N = 0.358 N.

 

The maximum buoyant force is:

1.152 N - 0.754 N = 0.398 N.

 

Buoyant Force:

0.368 ± .01 N

B) Displaced Fluid Method

 

 

Measure and record the mass of the empty beaker.  Place a flask filled to the top with water into the beaker.  Place the cylinder into the flask and allow the water to flow over the top and into the beaker.  Remove the cylinder and flask allowing the water that overflowed to remain in the beaker.  Measure the beaker plus water.  The buoyant force is equal to the weight of the water dispaced according to Archimede's principle. 

0.14999 ± 0.00005 kg	Mass of Empty Beaker (kg)
Trial	Mass of Beaker + Overflow Water (kg)		Mass of Water Overflow (kg)
1	0.18776 ± .00005 kg		0.03777 ± .0001 kg
2	0.18764 ± .00005 kg		0.03765 ± .0001 kg
Avg			0.03528 ± .002 kg

The minimum buoyant force is:

0.03671 kg * 9.81 m/s^2 = 0.36895 N

The maximum buoyant force is:

0.03871 kg * 9.81 m/s^2 = 0.37975 N

Buoyant Force:

0.374 ± .005 N

C) Volume of Object Method
Using this method, simply measure the cylinder's diameter and height using calipers and then calculate the volume.  Using the stated density of water (1000 kg/m^3), caluclate the weight of water that would be displaced by the cylinder and that would equal the buoyant force. 

Height of Cylinder:  0.0765 ± .00005 m
Diameter of Cylinder:  0.0254 ± .00005 m

pi * (0.0254 m / 2)^2  = 0.0005067 ± .000002 m^3

Area of Cylinder:  0.0005067 ± .000002 m^3

0.0005067 m * 0.0765 m = 0.00003874 m^3 ± .000002 m^3

Calculated Volume of Cylinder:  0.00003874 m^3 ± .000002 m^3
 

3.874 x 10^-5 m^3 * 1000 kg / m^3 = 0.03874 ± .002 kg

Mass of Water Displaced:  0.03874 kg
 

0.0374 kg * 9.81 m/s^2 = 0.380 N ± .02

Buoyant Force:  0.380 N ± .02 N

Conclusion:





The three values are the same within the experimental error.  The most accurate method was Experiment B (Displaced Fluid Method) with the error was only ± .005 N.  The error was based off of the scale measurments which have a precision to five decimal places.

In experiment A, had the cylinder been resting on the bottom of the container, it would have reduced the force read from the sensor.  The original force would have remained the same.  Since the buoyant force is the weight (in air) minus the weight (in water), it would have given a bigger buoyant force.