Poking Your Finger into a Cup of Water on a Scale: Simple Adhesion Force Experiments

Abstract

Newton’s laws are a ubiquitous topic in introductory physics instruction. One common problem involves asking what will happen if you stick your finger into a cup of water sitting on a scale (Fig. 1). A way to solve the problem would be to first recognize that the water exerts a buoyant force upward on the finger, which students can recognize as being the reason why they feel lighter when they are in a swimming pool. By Newton’s third law, the finger must hence exert a downward-pointing force on the water (labeled FB in Fig. 2). Since the water is not accelerating, the normal force from the beaker acting upward on the water (FN2) must increase to equal the sum of the weight of the water (FW) and FB (Newton’s second law). By Newton’s third law, the water must exert a force equal to FN2 down on the beaker. However, since the beaker is not accelerating, Newton’s second law tells us that the normal force from the scale is equal to this increased FN2. Via these chains of Newton’s second and third laws, we can see that the reading on the scale will increase.