Buoyancy of Objects
Goal: To determine the density of an object
When an object is submerged
in a fluid, the
interaction between the fluid and object causes the object to
experience an upward push. If the density of the object,
ρ, is less than the density of the fluid,
object would float in the fluid. If ρ > ρfluid, the
object would sink. In both cases, the object displaces volume of water equal to the submerged volume. When the object sinks, it is fully submerged,
and the volume of the displaced water is equal to the entire object's volume.
In this lab experiment, we will
use this principle to determine the volume of an unknown
object. The mass of the object will be measured using mass
scales, and the density then will be calculated using the formula:
- Propagation of uncertainty in the measurements.
uncertainty in the measurements arises from the precision of the
instruments used. The precision of an instrument is defined as the smallest unit marked on that instrument. Thus for example, if the mass scale gives the mass of an object in a x.xxx g format, the precision of that scale is 0.001 g. A measuring tape which can measure lengths in format x.x cm, will have a precision 0.1 cm.
As we multiply, divide, add or subtract various measurements, the uncertainty in the results accumulates. Here are two simple rules about how the uncertainty propagates throughout the calculations.
- Addition or subtraction of two measurements, a ± Δa and b ± Δb.
If c = a ± b, then the absolute uncertainty in c is
Δ c = Δ a + Δ b.
Note, that even if c = a − b, the absolute uncertainty is still the sum of the two. We cannot cancel uncertainties, they only accumulate in any mathematical operation.
- Multiplication or division of two measurements, a ± Δa and b ± Δb.
If c = a × b or c = a ÷ b, then the fractional uncertainty (the percent error) in c is:
Note, that regardless of whether it is a multiplication or division, the fractional uncertainty is still the sum of the two.
- Activity 1: Determine the density of an unknown object.
- You need:
- A graduated cylinder and an unknown object. (This will be provided by the instructor).
- A measuring tape
- Measure the mass of the object and the volume that it displaces. Record the values in the table below, including the absolute and relative precision of the mass scale, Δ m.
- Results:Write down your final result in the format:
Using the values for the densities of various metals in the
textbook, answer the following questions:
- Can the material be Aluminum?
- Can the material be Iron?
- Would the object flow if submerged in Mercury?
- Which measurement contributes the most error to the final result?
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Created: Fri Jul 20 16:47:28 Eastern Daylight Time 2007
Last modified: Wed Oct 24 20:41:30 Eastern Daylight Time 2012