PhysicsLAB: Density of an Unknown Fluid

This lab makes use of rotational equilibrium and buoyant forces to determine the density of an unknown fluid.

The equipment needed includes: a meter stick pivoted at its center of mass, a triple beam balance (or digital scale), an known mass (a 100-gram hooked mass), a mass hanger (50 grams), a 100-gram slotted mass, a graduated cylinder, a Styrofoam cup, water, and some oil with an unknown density.

The first part of the lab involves calibrating the equipment, then you will calculate the oil's unknown density using water as your standard.

Part I: Calibration

Initially, submerge the 100-gram hooked mass into a given volume of water in a graduated cylinder to measure its volume using Archimedes' Principle. Once you have your readings, remove the mass from the water and dry it off.

What was the initial water level in graduated cylinder (in ml)?

What was the final water level when 100-gram hooked mass is submerged (in ml)?

What is the effective volume of the 100-gram hooked mass (in cm³)?

Now suspend the 100-gram hooked mass to the right string at a distance L from the meter stick's center of mass (pivot point). Then suspend the slotted mass hanger from the left string the same distance L for the stick's center of mass. Place the 100-gram slotted mass on the slotted mass hanger. Make sure that the slotted mass hanger is sitting in the center of the balance's pan and adjust the sliding riders (make sure that any riders on the notched beams are securely in a notch) until the meter stick returns to equilibrium. Then determine and record the reading on the balance.

What does the triple beam balance read in grams?

Why was it necessary to bring the meter stick to equilibrium before reading the triple beam balance?

Now submerge the 100-gram hooked mass in distilled water by filling the Styrofoam cup with sufficient water to completely cover the mass without it resting against any of the cup's sides or bottom. Once again, slide the riders along the beams (make sure that any riders on a notched beam are securely in a notch) until the meter stick returns to equilibrium. Record the new reading on the triple beam balance.

What is the new reading on the triple beam (in grams) while the 100-gram hooked mass is submerged in distilled water?

The difference in the two triple beam balance readings indicates the buoyant force of the distilled water on the 100-gram hooked mass. Use that difference and the volume of the cylinder to calculate the density of water.

What was your experimental density of distilled water in g/ml?

Notice that the density of "pure water" takes on a maximum value of 1.000 g/ml or 1000 kg/m³ at 4ºC.

Using a thermometer, what was the temperature of your distilled water in ºC?

By referencing the chart displayed above (based on data taken from this page), determine the accepted value for the density of the distilled water you used in this experiment.

What was your experiment's percent error?

Part II. Determining the density of an unknown oil

Remove the 100-gram hooked mass from the water and dry it off without changing its moment arm (lever arm). Now your teacher will provide a cup of oil having a sufficient depth to cover your 100-gram hooked mass.

Once again, balance your triple beam until the yardstick returns to equilibrium, and read the balance.

What was the reading on the balance (in grams) while the 100-gram hooked mass was submerged in oil?

Using the volume of the 100-gram hooked mass, your final reading of its mass when the 100-gram hooked mass was submerged in oil, and the equation for buoyant force, determine the density of the oil.

Based on your error from your distilled water trial, what is a probable range of values for the oil's density?

If this oil and distilled water were to be mixed together which of the following would occur?

they would remain mixed
all of the oil would eventually sink below the water
all of the oil would eventually rise to the top of the water

Justify your previous answer.

Conclusions

Based on the actual density of the water used in this experiment, what was the true mass of the 100-gram hooked mass in grams? (Be accurate to 2 decimal places.)

What is the experimental density of the 100-gram hooked mass in g/cm³

Based on the density table provided on this page, the 100-gram hooked mass could have been made from which metal(s)?