Physics 250 Laboratory: Buoyancy

Transcription

1 Physics 250 Laboratory: (Fluids) Score: Section #: Name: Name: Name: Lab-Specific Goals: To learn about density and buoyancy through experimenting with these concepts. Equipment List: Graduated cylinder Plastic cups Pasco force meter and GLX (or spring scales) Scale or triple-beam balance (scale at back of room) mass set Water (sink in room) Plastic tray Thread/string Ruler mass set: Al, Brass & Steel solids, clay, several piece of wood Introduction and Pre-Lab Activity: Archimedes Principle is one of the oldest laws of physics. We have been studying laws (Newton s Laws of Motion, Conservation of Momentum & Energy) from the 17th and 18th centuries. Archimedes, one of the greatest mathematicians and scientists of all time, lived over 2200 years ago, and discovered how to calculate the buoyant force on an object (Archimedes Principle) and the principle of levers. According to ancient historians, Archimedes was able to build large machines that for at time defended his city of Syracuse against an attack the Roman army during the Second Punic Wars. One of Archimedes devices supposedly focused enough light on Roman ships to burn them down (Mythbusters (Discovery Channel) examined this one and claimed it busted, and then challenged

2 their viewers to see if they could succeed. For more information, check out After a 2-year siege, the Romans finally won and Archimedes was killed by a Roman soldier despite the Roman general s orders that Archimedes be unharmed, so that the Romans could gain his expertise in machines. 1) We will be putting various objects in water (some may float, some may sink). Let s first consider an object that is submerged in water and hanging from a string with tension T. Draw free-body diagrams for the object hanging from the string when it is outside the water (left) and submerged in water (right). IN AIR SUBMERGED IN WATER 2) From your free-body diagrams, determine how to calculate the buoyant force on the metal when it is in water from the tension in the string in the two situations above. State below how you would do this. 3) What is the buoyant force acting on an object of mass M that is floating? (Of course, in this case, there would be no tension in the string.)

3 Introductory Activity: Using the Force Probe & GLX to Measure Buoyant Force 1) Turn on the GLX. 2) From the home menu (press the key that looks like a house to get there), select digits. 3) If the top box does not display Force, pull positive (N) : (a) Press and use the arrow keys to select the top box. (b) Press again, use arrow keys to find and to select Force, pull positive (N) 4) If the GLX does not display two decimal places on the right, then: (i) Press and select the top box with the arrow keys (ii) Press to open the menu, select Data Properties (iii)scroll to Number of Digits and increase to 2 using the + button. (iv) Press F1 ( ) to select this change 5) Press ZERO button on front of force sensor to tare (zero) the sensor. (Reading should now be 0.00 N). 6) Take the metal weight on the thread and hang it from the force meter and record its weight in the table below. 7) Partially fill a cup with water. Lower the metal into the water until the metal is completely submerged (but not touching the bottom of the cup). What is the apparent weight (the tension in the thread) of the metal now? (Record this value below.) Force (N) Table 1. Forces on metal weight Weight of Metal Apparent Weight of Outside Water Metal Inside Water 8) In the pre-lab, you figured out a way to calculate the buoyant force from the two tensions in the thread (i.e., the weight outside water and the apparent weight inside water). Show your calculations in the space provided and write your calculated value of the buoyant force on the line below. Buoyant force A few experimental notes: (1) Do all your experiments on the tray when possible to keep water away from the equipment (GLX). (2) Dry everything immediately after removing it from the water. Your station should be dry and cleaned up before you leave the lab. (3) The density of water is 1 g/cm 3 = 1000 kg/m 3.

4 Activity #1. Buoyant force is weight of fluid displaced. Activity 1a. The buoyant force acting on an object in a fluid equals the weight of the fluid displaced, not the weight of the submerged part of the object. 1. Pick one of your largest masses and determine its weight using the force probe and enter it below. 2. Determine the volume of your object and enter it below. 3. Submerge different fractions of this object in water (see below) and determine the buoyant force on the object. Calculate the weight of the object that is submerged (e.g., if ¼ of the object is submerged, that weight would be ¼ the weight of the object). 4. Calculate the weight of the of the displaced fluid using the density of water and the volume of the object that is submerged) Weight of object: N Volume of object: m 3 ¼ ½ ¾ 1 Fraction submerged Volume submerged (m 3 ) Weight of object submerged (N) Weight of water displaced (N) Force reading when object in water (N) Buoyant Force on object (N) Discuss your results: which weight best matches the buoyant force you found? The weight of the object submerged or the weight of the fluid displaced? Justify your answer from your data. Is this consistent with Archimedes Principle?

5 Activity 1b: The buoyant force doesn t depend on the depth of the object (as long as it s fully submerged) in an incompressible fluid such as water. 1. You will want your container as full of water as possible without causing it to spill. 2. Pick a mass that is a good deal smaller than the container (so it can be lowered far beyond the surface). 3. Measure the buoyant force when the top of the object is just below the surface. 4. Lower the object all the way to the bottom (but not touching the bottom) and measure the buoyant force. 5. Now measure the buoyant force at a midpoint between these two measurements. How far lowered Just below surface Just above bottom Midpoint Force reading when object in water (N) Buoyant Force on object (N) From your data, what can you say about how the buoyant force depends on how far down the object is in the fluid (when it is fully submerged)? Is this consistent with Archimedes Principle? Activity 1c: The density of the object does not set the buoyant force for a fully submerged object. You should have two objects that are the same size, but made of different materials. Find their buoyant forces when completely submerged. Should they be the same or different based on Archimedes Principle? Are your results consistent with Archimedes Principle? How far lowered Object 1 Object 2 Force reading when object in air (N) Force reading when object in water (N) Buoyant Force on object (N)

6 Activity #2: Role of density in buoyancy in floating/sinking Floating/Sinking (for a solid object) depends on the density of the object, an inherent property of the material, and the density of the fluid. Activity 2a. Floating and size. 1. Find two pieces of wood or plastic that are the same material but different sizes (one should be about double the size of the other). 2. Put the smaller one in water and estimate the % of the object that is submerged. 3. Now put the larger one in water and estimate the % of the object that is submerged. Smaller piece: % submerged =, Larger piece: % submerged = Did the % submerged depend on the object s size? Does this mean that the buoyant force doesn t depend on the weight of the object? (Do the two pieces have the same buoyant force?) Explain carefully being sure to use Newton s Second Law (including free body diagrams) and Archimedes Principle in your answer. Activity #3: Buoyant force and apparent weight of container 1) Pick two different masses from your mass set and weight each one in the air. 2) Weigh each mass completely submerged in water. Calculate the buoyant force on each object. 3) Bring your water cup and the two masses to the scale in the back of the room. Measure the weight of the water cup (with the water in it). 4) Then submerge each mass (separately) in the water cup and measure the weight of the cup while the mass is submerged in the water (but not touching the bottom). Object weight in air (N) Object weight in water (N) Buoyant force on object (N) Weight of water cup (N) Weight of water cup with object submerged in it (N) Increase in weight of the water cup (N)

7 What happened to the apparent weight of the water cup when something was submerged in the water? How did that change compare to the buoyant force the water exerted on the object submerged in it? Explain what you observed using Archimedes Principle, Newton s Second & Third laws. (Hint: a free-body diagram of the water cup will be very helpful.)

8 End-of-Lab Questions Answer these questions and give a brief justification of your answer. Use density of water = 1000 kg/m 3 = 1 g/cm 3 ; 1 ml = 1 cm 3 1) What can we say about the displaced fluid for a floating object at rest? A. It has the same volume as the object B. It has the same weight as the object C. It produces no buoyant force D. Both A and B E. Both B and C 2) What can we say about the displaced fluid for a completely submerged object that is at rest? A. It has the same volume as the object B. It has the same weight as the object C. It produces no buoyant force D. Both A and B E. Both B and C 3) A 0.02 m 3 object has a density of 2700 kg/m 3 and is submerged in water. What is the buoyant force on the object? 4) What is the apparent weight of the object from question #3? 5) A 0.06 m 3 object has a density of 5000 kg/m 3 and is 2/3 submerged in water. What is the buoyant force on the object?