- 2 When The Cylinders Are Placed In The Unknown Liquid The Force Probe Measures 0 719 N For The Aluminum Cylinder And 1 1 (32.82 KiB) Viewed 54 times
Part 1: Show that the buoyant force Fg is equal to pg V by first calculating pgVand then by measuring Fg indirectly using the force probe. + The volume of a cylinder is Vcylindor=Rh, where is the radius and his the length (or height). When you measure the length h and diameter of each cylinder, there will be some uncertainty. The uncertainty i the length we'll call on and the uncertainty in the diameter we'll call op. You will measure the length of the cylinder using the ruler, shown below. Since the scale is in centimeters and the tick marks are each 1 mm 1 mm = 0.001 m is a good estimate for the uncertainty, e.g. on = 0.001 m. The diameter has been measured for you using vernier calipers to reduce the uncertainty to ap = 0.0001 m. The uncertainty on each of thes needs to be propagated to the uncertainty on the volume, and the formula is oy=v( 200+, .). Finally, the uncertainty on the volume and the uncertainty on the mass need to be propagated to the uncertainty D h on the density. The density is the usual p = m/Vand the uncertainty is 0,- OV + V P (** om). לת Shown below are the cylinders next to rulers. The numbers on the rulers represent cm. Measure the length of each cylinder and put those values in the table below. Then determine the uncertainty of those measurements (note that the uncertainty for each will be the same). Then fill in the rest of the table using the formulas stated above. Here's the aluminum (Al) cylinder: 123456789 Here's the lead (Pb) cylinder: : 1. What is your estimate for the uncertainty on the length in meters? on = .001 m Quantity Al Pb .085 = .001 .034 $ .001 Length (m) Diameter (m) 0.0234 + 0.0001 X Volume (m) .000036 # + 29.83 Your answer is too high. 0.0212 + 0.0001 .00003085 Your answer is too high. £ .00001 Your answer is too high. 0.1361 = 0.0001 11343.95 $ 0.01 Your answer is too low. Mass (kg) 0.0987 0.0001 2671.37 + 0.01 Your answer is too low. x X Density (kg/m)