Archimedes Principle

Transcription

1 Objectives Archimedes Prciple In this lab you will Equipment use Excel to plot mass and volume data for water to obta its density. use Archimedes Prciple to measure the densities of Lucite, lead, and wood. measure weight usg the Vernier Force Sensor. plot your data and analyze it usg the Vernier Logger Pro software. Vernier Force Sensor, Vernier LabPro system (cludes computer and Logger Pro ), graduated cylder, solid Lucite cylder, lead sker, wooden block, support bracket (clamped to a small stand), clamps, plastic beaker, scale, and strg. Theory The density ρ (Greek letter rho) of any material is defed as m ρ = Equation 1 V where m is the mass of a sample of the material and V is its volume. By varyg the size of the sample you will obta different masses m 1, m 2, correspondg to different volumes V 1, V 2, When you plot your mass data along the y axis and your volume along the x axis, you will fd that the pots tend to follow a straight le of slope equal to the density sce m = ρv from Equation 1, i.e. the equation has the form y = ax + b. Another method of measurg density volves fully immersg the sample a fluid, such as water. The sample experiences an upward buoyant force; as a result, it appears to weigh less accordg a standard scale (see Figure 1). scale measures w out scale measures w < w out sample mass w out w out B buoyant force Figure 1 Page 1 of 5

2 Let w out denote the weight measured when the sample is outside of the fluid (i.e. its true weight) and let w denote the weight measured when the sample is side the fluid (i.e. itse apparent weight). Then the magnitude of the buoyant force B is simply the difference between these two weight measurements: B = w out w Equation 2 Accordg to Archimedes Prciple the buoyant force also equals the weight of displaced fluid, or B = w f. Use Equation 1 to express w out = ρvg and w f = ρ f Vg so that w out /w f = ρ/ρ f. With Equation 2 we can write the ratio w out /w f as w out /(w out w ). Therefore, ρ/ρ f = w out /(w out w ), or w = ρ w w f out ρ Equation 3 out Procedure I. Determg the Density of Water 1) Use the scale to measure the mass of the graduated cylder. Record its mass ( grams) on your data sheet. 2) Fill the cylder with 100 ml of water and measure the total mass. Repeat for 200, 300, 400, and 500 ml of water. Subtract the mass of the graduated cylder from each value and record your results on your data sheet. 3) Open Excel and plot your data (see the Theory section). Add a trendle and compute the slope which equals the density of water ρ water g/cm 3. (Note that 1 cm 3 = 1 ml.) You will use this value of ρ water Part II. Prt your graph. II. Determg the Densities of Lucite, Lead, and Wood 1) Screw down a clamp to the support bracket then fasten the handle of the force sensor to the clamp. Make sure to select the ±10 N settg on the sensor. Now hang the Lucite cylder by a strg from the sensor s hook. Adjust the clamp until the strg is completely vertical (see Photos 1 and 2). 2) Connect the force sensor to the LabPro terface and then open Logger Pro on your computer. A Force-Time plot should appear; delete any other plots that are shown. Click the Collect button to test the quality of your data. Make sure that your data is collected for no more than 2 seconds (see Graph 1). Also check that the collection rate is is at least 30 data/sec. 3) Click the Collect button to measure the weight of the Lucite cylder outside of the water. You should obta a flat le for your Force-Time plot. A significant amount of jitter your data implies that the sensor and/or the Lucite is vibratg. Re-adjust your set-up and try aga. Use the R button to fd the y tercept and record its value on your data sheet. Page 2 of 5

3 Photo 1 Photo 2 4) Fill your graduated cylder with 350 ml of water and then lower the Lucite to it. Make sure that the Lucite is fully submerged. Repeat Step 3. Use Equation 3 to calculate the density g/cm 3 and the percent error. 5) Replace the Lucite cylder with the lead sker and repeat Steps 2 4. * * * * * The procedure must be slightly modified order to measure the density of the wooden block because it floats water. 6) Replace the lead sker with the wooden block and repeat only Steps 2 and 3. Record its weight as w. 7) Now attach the lead sker with a piece of strg to the bottom of the wooden block (see Photo 3). Fill at least half of the plastic beaker with water and then lower the block and sker until the sker only is fully submerged. Repeat Steps 2 and 3 (see Photo 4). Record the weight this case as w. 8) Now lower the block + sker until both objects are fully submerged. Repeat Step 3. wd Record the weight this case as w. Complete the rest of the calculations. Each student is required to submit a completed data sheet order to receive full credit. Your lab group needs to submit only one Mass-Volume graph. This graph is to be stapled to the data sheet of one of your lab partners Each lab partner does not need to submit his/her own graph. Page 3 of 5

4 Photo 3 Photo 4 Graph 1 Page 4 of 5

5 Data Sheet Archimedes Prciple Name Date Partners Names I. Determg the Density of Water Mass of graduated cylder (w/o water) = grams Volume [ml] Mass [g] Measured density of water (slope of Excel trendle) = g/cm 3 Accepted density of water = 1.00 g/cm 3 Acc Meas Percent error = 100 = Acc % II. Determg the Densities of Lucite, Lead, and Wood Accepted density of Lucite = 1.19 g/cm 3 Accepted density of lead = 11.3 g/cm 3 Material Lucite Weight Out w out [N] Weight In w [N] Density ρ [g/cm 3 ] % error Lead Weight of wood alone out of water w wd-out = N Weight of wood and sker, sker w = N Weight of wood and sker, both w = N wd Use Equation 3 (modified): wd out ρ w ρ = = g/cm 3 w w water wd out wd Page 5 of 5