Laboratory: Archimedes' Principle, Exercises of Physics

Download Laboratory: Archimedes' Principle and more Exercises Physics in PDF only on Docsity! Phy1401: General Physics I Laboratory Page 1 of 4 Laboratory: Archimedes' Principle Introduction: Eureka!! In this lab your goal is to perform some experiments to understand the source of Archimedes’ excitement when he discovered that the buoyant force on an object in a liquid is equal to the weight of the liquid that the object displaces. Archimedes made his discovery without the benefit of Newton's insights. He was arguably the premier scientist of antiquity. Since you have Newton's achievements as part of your intellectual heritage (Phy211) we'll use the concepts of force and equilibrium to measure the buoyant force acting on a (partially or totally) submerged object. Here is the idea behind the experiment. Suppose we hang a small mass from a force sensor, arranged in the configuration shown in the figure below. The bob in the liquid may be partially or totally submerged. H2O Force Sensor mass graduated cylinder According to Archimedes, the upward buoyant force (FB), which the liquid exerts on the object, is equal to the weight of the fluid displaced or: FB = mfluidg = (ρfluidV)g (1). It should be noted, the buoyant force produced by the displacement of fluid in the cylinder will result in a reaction force of equal but opposite magnitude exerted by the bob on the liquid (according to Newton’s 3rd Law). We will use this action-reaction relation to measure the buoyant “reaction” force with a standard digital scale. While the mass is hanging, the force sensor will measure the tension in the string (FT1), which should be equal to the weight of the suspended mass. Applying Newton’s 2nd Law to the hanging mass: FNet = FT1 - mg = 0 Or FT1 = mg (2). When the mass is inserted into the liquid, the force sensor will measure the new tension in the string (FT2) which should be equal to the weight of the mass minus the buoyant force, FB. Thus, when we look at the forces acting on the hanging mass: FNet = FT2 - mg + FB = 0 or FB = mg – FT2 = FT1 – FT2 = ΔFT (3). Combining equations (1) and (3), the relationship between the buoyant force, the normal force (from the scale) and weight of the cylinder and liquid is given by: Phy1401: General Physics I Laboratory Page 2 of 4 FB = FT1 – FT2 = (ρfluidV)g or FB = FT1 – FT2 = (ρfluid.g)V (4). finger cup Scale liquid Thus the buoyant force is linearly related to the displaced volume of the fluid, V, and the slope of a graph of FB vs V should yield ρfluid .g. The Experiment: Part 1: Qualitative Observations 1) Obtain a digital scale and zero it. 2) Obtain a Styrofoam cup and fill it halfway with water. 3) Place the cup on a digital scale. Observe the scale reading. Record it: ______________ 4) Insert your finger partially into the water. Observe the scale reading and record it: ______________ 5) Insert finger further into the water. Observe the scale reading. Record it: ______________ 6) Insert finger even further into the water. Observe the scale reading. Record it: ______________ Question: How does the scale reading change as your finger is submerged into the water?