Pressure Paradox

Introduction

Can you “feel” the weight of two different objects correctly? If one object feels heavier, does it actually weigh more? In this demonstration, the distinction between weight and pressure is observed.

Concepts

• Pressure
• Weight

Materials

Safety Precautions

Although this activity is considered nonhazardous, please follow normal laboratory safety guidelines.

Disposal

The materials may be saved for future use.

Procedure

1. Give each student group one steel ball and one Styrofoam ball.
2. Ask a student from each group to hold the steel ball in the palm of one hand, and the Styrofoam ball in the palm of his or her other hand.
3. Which ball feels heavier? Have the students compare the apparent weight of the two balls. They may want to toss them in the air a few centimeters and catch them to get a better “feel.” The students should keep their observations to themselves until all the students have an opportunity to compare the weights of the balls.
4. Repeat steps 2 and 3 for the additional students in each group until all the students have compared the weights of the two balls and determined which one feels the heaviest.
5. By a show of hands, ask the students which ball they believe is heavier—the steel or the Styrofoam. Tally the number of students who believe the steel ball weighs more and those who believe the Styrofoam ball weighs more.
6. Next, have the students weigh the Styrofoam ball with a balance. Then, have them weigh the steel ball. (A weighing dish may be necessary to prevent the balls from rolling off the weighing pan). Which ball actually weighs more?
7. Discuss the observations and measurements with the students. Why does the steel ball feel heavier even though the Styrofoam ball weighs more? Consider using the discussion material below.

Teacher Tips

• This kit contains enough materials for a class of 30 students working in groups of six or five groups of students: 5 steel ball bearings and 5 Styrofoam balls.
  
• Locate other materials that may give deceptive pressure versus weight relationships, such as racket ball and a wood block of the same mass.
  
• If students do not feel a weight difference, try this variation: Wrap the Styrofoam ball in aluminum foil (to give it a little extra weight). Then, have students determine which is heavier—two steel balls, or one aluminum-covered foam ball. Preweigh the aluminum-covered ball to make sure it is slightly heavier than the two steel balls. Students will almost always say that the two steel balls weigh more.

Discussion

Pressure is a common term used every day to describe weather conditions. For example, barometric pressure is a measurement of the local air pressure and is used to help predict the weather. But, outside of measuring changes in air pressure, observing and quantifying pressure between objects is difficult. Pressure is defined as the amount of force exerted on a given area, or a force per unit area (F/A). Some common units of pressure are pounds per square inch (lb/in²), Newtons per square meter (N/m²) [also known as a pascal (Pa)], atmospheres (atm), and millimeters of mercury (mm Hg) (“millimeters of mercury” is the height of a small column of mercury that is held up by a pressure). A pressure exists whenever two objects are in contact with each other. The points of pressure only occur at the points of contact. The Earth’s gravitational force pulls all objects towards its center. However, there is no pressure until the object is in contact with the Earth, or with another object that prevents it from falling, and the pressure only exists at the contact points. The amount of pressure depends on the force and the surface area that the force acts over. The larger the area, the smaller the pressure for a given amount of force. A 10-lb ball and a 10-lb wood block both exert the same force due to gravity. A 10-lb ball, however, will exert more pressure on a tabletop than a 10-lb block of the same material because the round surface of the ball has a very small contact area with the tabletop compared to the larger rectangular surface of the 10-lb block. The force “feels” stronger when it acts on a smaller area because the force is more concentrated. The same amount of force acting over a larger surface area is spread out and “diluted” over the entire area so it “feels” weaker, even though it is the same force (weight).

This demonstration shows the difference between pressure and weight. The steel ball feels heavier than the Styrofoam ball when they are held side by side in each hand, but the Styrofoam ball actually weighs more. The Styrofoam ball has a larger curvature and makes contact with more of the palm’s surface. This lowers the pressure the Styrofoam ball exerts on the hand. The weight of the Styrofoam ball is spread out over the whole palm. The smaller contact area of the steel ball concentrates the weight and produces a higher pressure in the palm, even though it has a smaller mass. When the steel ball and Styrofam ball are held side by side, it feels as if there is more force on the palm holding the steel ball, and therefore more weight, when in actuality it is only a higher pressure.

References

Flinn Scientific would like to thank Mike Shaw, West Stokes High School, King, North Carolina, for providing us with the idea for this demonstration.