Experiment P18: Buoyant Force (Force Sensor)

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1 PASCO scientific Physics Lab Manual: P18-1 Experiment P18: (Force Sensor) Concept Time SW Interface Macintosh file Windows file Newton's Laws 45 m 300/500/700 P18 P18_BUOY.SWS EQUIPMENT NEEDED CONSUMABLES Interface water (800 ml) ±50 Newton force sensor vegetable oil (800 ml) - optional base and support rod beaker, 1000 ml calipers clamp, right-angle cylinder*, metal, with hook graduated cylinder lab jack mass set (for sensor calibration) ruler, metric string support rod * approximately 2 cm diameter and 6 cm long PURPOSE The purpose of this laboratory activity is to show that the buoyant force of an object depends on the volume of the part of the object that is submerged and to calculate the density of the fluid by plotting the buoyant force versus the depth of the submerged part of the object. THEORY According to Archimedes Principle, the buoyant force on an object wholly or partially submerged in a fluid is equal to the weight of the fluid displaced by the object. F b = m f g = ρ f Vg where ρ f is the density of the fluid, V is the volume of the object that is submerged, and g is the acceleration due to gravity. Since the volume is equal to the cross-sectional area, A, multiplied by the submerged height, h, the buoyant force is given by F b = ρ f (Ah)g If the object is lowered into the fluid while the buoyant force is measured, the slope of the graph of F b versus h is proportional to the density of the fluid. dg 1996, PASCO scientific P18-1

2 P18-2: Physics Lab Manual PASCO scientific PROCEDURE For this activity, the force sensor measures the buoyant force on an object as it is lowered into water. You enter values for the depth to which the object is submerged. The program plots buoyant force versus submerged depth. PART I: Computer Setup 1. Connect the interface to the computer, turn on the interface, and turn on the computer. 2. Connect the force sensor's DIN plug into Analog Channel A on the interface. 3. Open the document titled as shown: or Macintosh P18 Windows P18_BUOY.SWS The document will open with a Digits display of Force (Newtons) and a Graph display of Force (Newtons) and Depth (m). Note: For quick reference, see the Experiment Notes window. To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. Change the Experiment Setup window by clicking on the Zoom box or the Restore or Maximize button in the upper right hand corner of that window. dg 1996, PASCO scientific P18-2

3 PASCO scientific Physics Lab Manual: P The Sampling Options are as follows: Periodic Samples = Slow at 1 sec (one sample per second) and Keyboard input with Parameter = Depth and Units = m (meters). PART II: Sensor Calibration and Equipment Setup Sensor Calibration 1. To calibrate the force sensor, change the Experiment Setup window to full size by clicking on the Zoom box or the Maximize button in the upper right hand corner of that window. Full size Zoom box Restore button Minimize button Close box Control-menu button Maximize button Macintosh Reduced size Windows 2. In the Experiment Setup window, double-click on the force sensor s icon to open the Force Sensor setup window. dg 1996, PASCO scientific P18-3

4 P18-4: Physics Lab Manual PASCO scientific The Force Sensor setup window shows the default calibration values (50 Newtons produces 8 Volts, -50 Newtons produces -8 Volts). The force sensor is set up so that a pull away from the sensor is a negative force. For example, if a one kilogram object is hung vertically from the hook, the force sensor measures -9.8 Newtons (since the force is downward). 3. Mount the force sensor on a horizontal rod so the force sensor s hook is down. Do NOT put an object on the force sensor s hook yet. 4. For the High Value calibration point, press the tare button on the side of the force sensor to zero the sensor. Click the Read button for High Value. Since there is no object on the sensor s hook, type 0 as the High Value. 5. For the Low Value calibration, hang an object of known mass on the sensor s hook. 6. Click the Read button for Low Value. Enter the object s weight in Newtons (mass in kilogram x 9.8 N/kg). Remember, enter the object s weight as a negative value (a force pulling away from the sensor). Force Sensor Object of known mass dg 1996, PASCO scientific P18-4

5 PASCO scientific Physics Lab Manual: P18-5 In this example, the object has a mass of grams ( kg), or a weight of Newtons (entered as ). 7. Click OK to return to the Experiment Setup window. Equipment Setup 1. Mount the force sensor on a horizontal rod with the hook end down. 2. Measure the diameter of the metal cylinder. Calculate the radius (R) and the cross-section area (A). Record the crosssection area in the Data Table. Force Sensor A = πr 2 3. Hang the metal cylinder from the force sensor hook with a string. 4. Put about 800 ml of water into the beaker and place the beaker on the lab jack below the hanging cylinder. The bottom of the cylinder should be touching the water. 5. Position the metric ruler next to the edge of the lab jack. Note the initial height of the top of the lab jack. Beaker Lab jack Aluminum cylinder Ruler, metric dg 1996, PASCO scientific P18-5

6 P18-6: Physics Lab Manual PASCO scientific Preparing to Record Data Before recording any data for later analysis, practice entering values using the Keyboard Sampling window in the program. Click the REC button ( ) in the Experiment Setup window. The Keyboard Sampling window opens. The default value for Entry #1 is Arrange the Keyboard Sampling window and the Digits display of force so you can see both of them. Since the metal cylinder is not submerged, type in 0 as the depth. Click Enter to record the value. Your entered value appears in the Data list. The default value for Entry #2 is Type in (5 millimeters). Click Enter to record your typed in value. Your entered value appears in the Data list, and the new default value for Entry #3 ( or 10 millimeters) reflects the pattern of your previous entries Click Stop Sampling ( ) to end recording of your sample data. dg 1996, PASCO scientific P18-6

7 PASCO scientific Physics Lab Manual: P18-7 The Keyboard Sampling window disappears and Run #1 will appear in the Experiment Setup window. Erase your trial run of data. Select Run #1 in the Data list in the Experiment Setup window and press the Delete key on the keyboard PART III: Data Recording 1. When you are ready to begin data recording, press the tare button on the side of the sensor to zero the sensor. 2. Click the REC button ( ) to begin data collection. The Keyboard Sampling window opens. Type in 0 as Entry #1 for depth of submersion of the cylinder. Click Enter to record your typed in value. 3. Immerse the cylinder 5 millimeters (5 mm or m) by raising the beaker of water 5 mm with the lab jack. (Use the metric ruler to measure the distance that you raise the lab jack.) Type in for Entry #2. Click Enter to record your typed in value. 4. Increase the depth of submersion by increments of 5 mm. After each increase in the submersion, wait for the reading in the Digits display to become steady, then type in the new depth (in meters) in the Keyboard Sampling window. Click Enter (or press <enter> or <return> on the keyboard) to record your entered value. 4. Repeat the data recording procedure until the top of the cylinder is submerged. Click Stop Sampling to stop data recording. The Keyboard Sampling window closes and Run #1 appears in the Data list in the Experiment Setup window. ANALYZING THE DATA 1. Click the Graph to make it active. Click the Statistics button ( ) to open the Statistics area on the right side of the graph. Click the Autoscale button ( graph. ) to rescale the 2. Click the Statistics Menu button ( ) in the Statistics area. Select Curve Fit, Linear Fit from the Statistics menu. 3. Record the value of the slope (coefficient a2). dg 1996, PASCO scientific P18-7

8 P18-8: Physics Lab Manual PASCO scientific 4. Calculate the density of water by setting the slope equal to ρag and solving for ρ. 5. Compare the calculated value to the accepted value. DATA TABLE: Water Item Value Area (cross-section A = πr 2 ) m 2 Slope (from graph) ρ., Density of water (calculated) kg/m 3 ρ., Density of water (accepted) 1000 kg/m 3 Percentage difference % QUESTION 1. How does your experimental value compare to the accepted value for the density of water? OPTIONAL: DENSITY OF OIL 1. Repeat the data collection using vegetable oil instead of water. Compare the result for the density of oil to the value found from weighing a known volume (500 ml) of oil. DATA TABLE: Vegetable Oil Item Value Area (cross-section A = πr 2 ) m 2 Mass of 500 ml of oil + beaker Mass of beaker Mass of oil kg kg kg ρ., Density of oil (mass/volume) kg/m 3 Slope (from graph) ρ., Density of oil (slope method) kg/m 3 Percentage difference % dg 1996, PASCO scientific P18-8

9 PASCO scientific Physics Lab Manual: P18-9 OPTIONAL QUESTION 1. How does your experimental value for the density of oil compare to the value determined by the mass/volume method? dg 1996, PASCO scientific P18-9

where ρ f is the density of the fluid, V is the submerged volume of the object, and g is the acceleration due to gravity.

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