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# Which Weighs More: An Empty Cup or a full Cup?

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Source:
Author: Jerry Silver

### The Idea

Which weighs more: an empty cup or a full cup? Obviously, the full cup. So, if you turn a cup upside down with a flat cover, which has the better chance of being supported: the (lighter) empty cup or the (heavier) full cup? Many people find the outcome surprising.

### What You Need

• cup or beaker with a flat, circular, smooth top. (If the beaker has a spout, it should be flat enough so it can make contact with a card at all points along its top surface.)
• water to fill the cup
• flat, stiff, lightweight square, large enough to cover the entire top surface of the cup. The square should not become waterlogged. Cardboard is not the best choice. Foamboard stands up to water better. Index cards can work, but you must be careful not to let them flex and break the seal with the cup.

### Method

1. Start with the empty cup. Cover the empty cup with the square. Turn it upside down and observe what happens (Figure 36-1).
2. With the cup still empty, moisten the top surface of the cup to make it more sticky. Cover the cup and turn it upside down. What happens?
3. Now fill the cup with water to the brim. It won't hurt to have it go above the surface of the cup or to allow some water to spill out. Cover the cup with the square. Invert and observe what happens.

### Expected Results

The square will fall off with the empty cup, even with the benefit of the surface being sticky. The water in the full cup, however, will be held in place by the square (Figure 36-2).

### Why It Works

The water in a beaker 5 centimeters in diameter and 12.7 inches tall has a mass of 250 g (0.25 kg) and weighs 0.55 pounds (or 2.5 newtons). The air pressure on the 5 centimeter (roughly 2 inch) diameter circle is over 3 pounds. The air pressure is far greater than the weight of the water in the beaker. The empty beaker has the same pressure inside and outside the cup, so the air pressure is balanced and the weight of the cup causes it to fall. The adhesion of the square to the cup is clearly not enough to make up the difference.

### Other Things to Try

Calculate how tall the glass can be with the card supported by air pressure. (The density of water is 1 g for every cubic centimeter and 1000 g is the equivalent of 2.2 pounds.) Atmospheric pressure will support a column of water 34 feet high. Since mercury is more dense than water, atmospheric pressure will support a column of mercury about 30 inches high. The exact height varies with local air pressure and provides a way to measure changes in air pressure.

### The Point

Air pressure is large compared to the pressure exerted by the weight of a cup of water.