Part 2 Look at Figure 2. According to the theory developed in class, there is a unique angle 6 for which the wooden block will travel down the slope at constant speed. In this part of the lab, you are trying to nd the angle for which this happens. 1. Disconnect the two masses, and set aside the hanging mass. Place the wooden block plus 200g on top of the cardboard 2. Gradually raise the incline. Tap the block until it begins to move and stops. On sheet 2 of your excel le (look at the tabs on the bottom) Record this as your trial 1 minimum angle 3. Continue to raise the incline until the block moved with constant speed. Find the largest angle where the block is moving at constant speed. Record this as your trial 2 max 4. Repeat steps 2 and 3, recording the results as the trial 2 and 3 mins and maxes. 5. Take the average and standard deviation to get an experimental value for the angle and an uncertainty Friction Lab WriteUp Guide Turn in two things: 1. Excel book with everything in it 2. Document file Excel (xlsx file): Sheet 1: I Data for part 1 I Linest for part 1 I Graph with equation and reported value Sheet 2: I 10 trials to find the angle for part2 I Average value for the angle and standard deviation oftrials Sheet 3: I Calculation of hanging mass (min, max, best) and uncertainty Document (docx file [you may turn in a pdfonly if you are doing this whole thing in LaTeX, but I assume most of you are using word for this]): Section 1: I Derivation of,u either inserted as a sketch and hand~written work, or inserted as a sketch and then derived using equation editor I Copy ofthe graph from Excel file. Comment on the graph shape (does it match expectation) as well as on the ,u value (Report it as a number and uncertainty. Does it agree with what you know about ,u values?) Section 2: I Derivation of Angie I Derivation/calculation of theoretical uncertainty in the angle (use 6;; = 2266 > 66 = 63:36). Use the values of,u from part 1 and 3 from your theoretically derived result I Reported value of the angle : the uncertainty. The uncertainty should be whichever is bigger between the resolution ofthe instrument (if) and the standard deviation calculated on sheet 2. Make sure to let me know which source of uncertainty you are reporting. I Does your predicted theoretical value agree? (Do the i ranges overlap?) If so state that it does. If not state what you think is your biggest unaccounted for source of error ("operator error" is not an error. Be more specific}. Include a percent difference (theoretical experimental}/(theoreticaI) Section 3 I Derivation of mass I Derivation/calculation of uncertainty in hanging mass (easy error propagation. The uncertainty in the angle is small enough to ignore for this one} I Measured mass i uncertainty I Do they agree? The uncertainty in the angle mentioned in part 2 is a little hard. Remember that uncertainties are obtained by: =%M You will need to know that d(ta.n 6) _ 2 d9 sec 9 Angles must be measured in radians to use equations like that. Do all your calculations and then convert back to degrees Figure 1 cardboaxd sheet Figure 1 above shows the lab setup for part 1. Look at Figure 1. For a given m1, there is a mass mg for which the tension and friction forces on m1 exactly cancel and the system will move to with constant speed. In this lab, you will measure the values of 7711 (hereby referred to as the 'table mass') and 77m (which I will refer to as the hanging mass). We are trying to nd the values of the two masses which cause the block to move at constant speed. 1. Measure the mass of the wooden block 2. Set up the equipment as shown in Figure 1. The cardboard should be white side up. Set the wooden block on the cardboard and add an additional 200g. Record the total mass as the table mass in your data sheet. 3. Attach the 50g hanger and add mass. After adding mass, tap the wooden block to overcome static friction and observe what happens. You are looking for continuous, Sl motion 4. Find the value of the hanging mass for which the block moves an appreciable distance, but then stops shortly afterward. This is your minimum hanging mass 5. Find the value for which the mass begins to move at a slow, constant speed. This is your maximum hanging mass 6. Average the two masses, and then take the difference between the two and divide by 2. The average will serve as the best value and diff/2 is the uncertainty 7. Add 100g and repeat steps 3-7 until you have 5 data points Datapoint Table Mass (m_1, g) Min Hanging mass (m_2_min, g) Max Hanging mass (m_2_max, g) m_2 (avg, g) om 2 (diff/2, g) Mass of wood block: 377.63 377.63 71 71.5 0.5 Uncertainty of mass of wood block: 477.63 8 8 89 577.63 102 103 02.5 0.5 577.6 117 119 118 777.63 125 130 127.5 2.5 Table Mass versus Hanging Mass Calculated / average: 0.178 140.0 uncertainty 120.0 trials m1(g) m2(g) 8m1 6m2 OH 1 377.62 71.5 0.189 0.01 0.5 0.007019 y=0.141x+20.2 477.63 89.0 0.186 0.01 1.00 0.011257 3 577.63 102.5 0.177 0.01 0.5 0.004895 80. ge Hanging Mass (8) 4 677.63 118.0 0.174 0.01 1.00 0.008489 5 777.63 127.5 0.164 0.01 2.5 0.019621 60.0 # avg: 0.178 Su avg: 0.010256 40. 20.0 0.0 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00 Hanging Mass (8) slope 0.141 20.25417 intercept uncertainty 0.007571878 4.502921411 uncertainty 0.99142273 2.394437999 346.7616279 1988.1 17.2 = Part 1 Part 2 Part 3 +