Measurement procedure and experiment equipment
The device is a high thin transparent cylinder filled with an investigated liquid. At the top of the cylinder, there is a lid with an opening. We can drop a small-shot ball and observe its motion. It is not difficult to calculate the speed of the ball.
Friction force acts on a moving body in a viscous liquid. Amount of this force generally depends on many conditions such as liquid viscosity, a shape of a body etc. Stokes formulates the expression for the friction force F in case of a ball flowed round by unlimited laminar liquid:
,
(6.9)
where is a coefficient of internal friction; r is the radius of the ball; v is the speed of the ball.
Let us consider a ball dropped in a viscous liquid. There are three forces, which make the ball move (Fig. 6.3): 1) the gravity force:
,
(6.10)
where V is the volume of the ball; is the density of the ball; g is gravity acceleration;
2) the Archimedes force
(6.11)
where 1 is the density of the liquid in the cylinder;
3) the force of internal friction F (see formula 6.9).
According to the second Newton’s law
(6.12)
The speed of the ball being raised the force of internal friction increases and the acceleration of the ball slows down to zero. So the equation (6.12) for a steady motion of the ball becomes
.
Substitute
P,
and F
by
their equations (6.9), (6.10), (6.11)
(6.13)
Deduce from the equation (6.13)
,
where
( L is the distance between the scores; t is the time
the ball covers this distance).
Finally:
.
(6.14)
As a result, we must know the radius of the ball, the densities of the ball and the liquid and the time the ball passes the distance L.
Work procedure technique and data processing
Measure the radius of the ball by means of a microscope. Place the microscope on a white sheet against a sun light. Get a clear picture of a scale’s net by turning a limb of the microscope top lens back and forth. Get a clear picture of the ball by turning a limb of the microscope bottom lens back and forth. Count the number of pitches N on the scale net corresponding to the diameter of the small-shot ball. Scale factor c is written on the microscope body so it is possible to calculate the radius of the ball by the formula:
Repeat measurements 3 times turning the ball concerning to the scale. Calculate arithmetic mean r of three radii.
Set the observer’s eye against the upper score behind the cylinder. Drop the ball into the liquid stop; turn on a stopwatch just when the ball is passing the upper score. Remount the eye against the lower score and turn off the stopwatch just when the ball is passing the lower score. Write down the time of ball falling. Repeat measurements with 5-8 other small-shot balls.
Measure the distance between the upper and the lower scores L by a ruler.
Find the values of the ball and the liquid densities in the density table. The teacher gives material of the ball and the liquid.
Put the results down into table 6.2.
Calculate the internal friction coefficient for each ball by the formula (6.14).
Calculate these coefficient errors as direct measurement errors.
Table 6.2.
Exp. № |
r, m |
t, s |
η,
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Δηi |
Sn |
Δη |
1 |
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2 |
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3 |
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4 |
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5 |
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