Apparatus and Procedure
Overview of Operation
This experiment consisted primarily of performing a series of trials in which a weighted
cylinder was dropped vertically through a pipe. The pipe was rigidly attached to a lab
bench by two metal supports. Near the two supports, optical sensors were placed on the
pipe. The optical sensors were used to measure the velocity of the falling cylinder. The
entire length of the pipe was approximately 8 feet, but was divided into several
noteworthy segments. The segment of pipe from the top opening to the top optical sensor
was 70 in. long and slightly curved. The remaining segments of the pipe were not
curved. The segment of pipe from the top optical sensor to the bottom optical sensor was
26 in. long. The segment of pipe from the bottom optical sensor to the end of the pipe
was 7 in. long. The lower section of the pipe was dubbed the “snubbing section” because
its smaller diameter caused the falling cylinder to slow down. The inner diameter of the
snubbing section was 1.779 in., while the inner diameter of the upper section was 1.9 in.
The length of the snubbing section was 27.89 in. A small pulley wheel was supported 6
in. above the top opening of the pipe. The cylinder was hollow metal and had a
removable lid that allowed small metal pellets to be added or removed. The cylinder was
6 in. long and had a diameter of 1.75 in.
Conduct of the Experiment
Twelve separate trials of releasing the cylinder were performed. The cylinder was
dropped from 4 different heights for 3 different masses. The four heights were at 1.5 ft.
intervals, starting from the top opening of the pipe. The three masses of the cylinder were
218 g, 622 g, and 1162 g. Experimental data were recorded by the Chart Recorder
software program on three channels. The two optical sensors recorded a voltage that was
interrupted only when the cylinder passed in front of the sensor. The time interval
between consecutive interruptions in the voltage reading corresponded to the times when
the top and bottom surfaces of the cylinder passed in front of the optical sensor.
Additionally, there was a pressure gauge at the bottom of the pipe. The pressure increased
to a peak value when the cylinder first deflected and started going back up the pipe. The
pressure reading reached a final value when the cylinder slowly settled down to the
bottom of the pipe. The peak and final pressures were used to compare the theoretical
model with the experimental data.
Results
It was desired to experimentally determine the velocity of the cylinder as it struck the
bottom of the pipe. It was assumed that this velocity was the same as the velocity of the
cylinder while it was passing the bottom optical sensor. This velocity was calculated by
dividing the cylinder length by the time interval of the cylinder passing in front of the
sensor. A graph of cylinder impact velocity at the bottom of the transfer line as a function
of the cylinder mass is shown in Fig. () for each of the release heights.
Impact velocity VS Cylinder mass
0.5
0.45
0.4
Velocity (m/s)
0.35
0.3
Max height
2nd height
3rd height
4th height
0.25
0.2
0.15
0.1
0.05
0
0
200
400
600
800
1000
1200
1400
Mass (g)
Figure 2: Cylinder impact velocity vs. Mass, for 4 heights
Next, it was desired to find the point at which the cylinder deflected (came to a complete
stop and began to reverse direction). The cylinder velocity immediately before the
deflection was approximated as the velocity at the top optical sensor. By using this
assumption, any transient velocity was ignored. The velocity at the top optical sensor was
calculated by dividing the cylinder length by the time interval that the cylinder passed in
front of the sensor. This velocity was multiplied by the time interval between the cylinder
reaching the top optical sensor and the peak pressure. This value was the distance
between the top optical sensor and the point of deflection. The distance from the top
optical sensor to the deflection point is graphed in Fig 3, for each of the masses.
Distance from top sensor vs Mass
0.45
0.4
0.35
Distance (m)
0.3
0.25
0.2
0.15
0.1
0.05
0
0
200
400
600
800
1000
Mass (g)
Figure 3: Distance before deflection vs. Mass
1200
1400
Peak Pressure vs Height
60000
50000
Pressure (Pa)
40000
1162
622
218
30000
20000
10000
0
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
Height (m)
Figure 4: Peak Pressure vs. Release Height, for 4 masses
Discussion
As shown in Fig. (), the release height of the cylinder had very little effect on the impact
velocity. The cylinder mass, however, had a much more profound effect. The average
impact velocities for the 218 g, 622 g, and 1162 g masses were 0.087 m/s, 0.236 m/s, and
0.419 m/s, respectively. Increasing the mass of the cylinder increases the velocity at
which the cylinder hits the bottom of the pipe.
The distance from the top optical sensor to the point of deflection (Fig 3) shows a similar
trend as the impact velocities. As mass increases, the cylinder travels farther down the
pipe before it is deflected.
Although the release height had little effect on the impact velocity, the height greatly
affected the peak pressure. The 1162 g cylinder showed the largest change in peak
pressure due to increasing the release height, while the 218 g cylinder had only a small
change in peak pressure due to increasing the release height.