Sticking a Plastic Sheet to a Table

Let's take a look!

Watch the video on YouTube.

What type of experiment is this?

Experimental procedure and explanation:

• Affix a suction cup to a plastic sheet (18 cm × 25 cm) and place the plastic sheet on a table with the suction pad on the top. Rub the top with a towel so that there are no gaps between the plastic sheet and the table.
• Attach a spring scale to the suction cup and pull upwards. The plastic sheet does not move at all, even when it is pulled with a force of approximately 5 kg.
• Next, see how much force a smaller plastic sheet (12 cm × 18 cm) can withstand. The plastic sheet comes off the table with an applied force of approximately 16 kg. From this experiment, it is clear that even the small plastic sheet can support a large force.
• The principle of this is often explained as follows: “Atmospheric pressure is acting on the top side, and there is a vacuum under the plastic sheet, so it can support a large force. This shows how strong atmospheric pressure is.” However, if this explanation were correct, the force of atmospheric pressure acting on each 1 cm² would be approximately 1 kg, and therefore this plastic sheet would be able to support a force of approximately 216 kg; however, in our experiment, the applied force was approximately 16 kg, which is a difference of more than one order of magnitude.
• At first glance, the plastic sheet appears to be smooth and perfectly flat, but if we look through a microscope, we can see that there are tiny bumps, waves, and warping on the surface. The same is also true for the surface of the table. When these two surfaces come into contact, there are gaps between them as shown in the figure, and only a few parts of the plastic sheet and the table are actually in solid contact. Unless the gaps are sealed, they are at atmospheric pressure, and therefore most of the bottom surface is at atmospheric pressure. When the plastic sheet is pulled upwards, the pressure of the contacting parts decreases. In theory, the pressure can drop to vacuum pressure; however, the plastic sheet usually comes off the table before the pressure drops to so low. At this time, only the parts of the plastic sheet and the table that are in solid contact have a contact pressure that is less than atmospheric pressure, and therefore the force supporting the plastic sheet is the difference between the contact pressure and the atmospheric pressure acting on the top of these parts only. The average value of the pressure on the bottom surface as a whole is thought to be approximately 90 to 95% of atmospheric pressure, which is far from a vacuum.
• In summary, at the parts where the plastic sheet is in contact with the table, which is only a small part of the total area, the pressure is less than atmospheric pressure, and therefore the force can be supported because of the difference between the contact pressure and the atmospheric pressure on the top surface. This force, which was approximately 16 kg in this experiment, is much smaller than the force due to atmospheric pressure acting on the top surface (approximately 216 kg for a 12-cm × 18-cm plastic sheet, meaning that only a small part of the force is due to atmospheric pressure.
• Although this is not shown in the video, a larger force acts on the plastic sheet when it is pulled up very quickly. This is because of the additional force caused by the viscous friction when air flows into the gap at the bottom, which depends on speed, as well as the additional force needed to accelerate the air near the bottom and top surfaces of the plastic sheet, which depends on acceleration.

[Note]	When performing an experiment that applies a force over 2 or 3 kg, be sure to conduct a safety check with a teacher. When considering the forces acting on an object under atmospheric pressure, be sure to consider the forces on the front and reverse sides, rather than on one side only. Mistakes are often found in introductory science textbooks, which commonly explain the operating principle here by saying that “it is pushed by atmospheric pressure”. This experiment is one such example.
[Keywords]	Atmospheric pressure
[Related items]	The Secret of Suction Cups, Sticking a Plastic Sheet to the Ceiling
[Reference]	“Illustrated Fluid Dynamics Trivia,” by Ryozo Ishiwata, Natsume Publishing, P16－17. “The Wonders of Flow,” Japan Society of Mechanical Engineering, Kodansha Blue Backs, P34－37.