y = 0.36x -6.1360501001502002503003504004500 200 400 600 800 1000 1200ms (g)mt (g)mt (g) vs ms (g) Teflon pan1) mp = Teflon pan = 62.6 g mp’ = Rubber bottom pan = 126.7 g 𝒎𝒕 = mp + m = 62.6 + 200 = 262.6 g Using Linest, S 0.36 -6.136 B δS 0.013875 9.996312 δB m (g) ms (g) mt (g) 200 80 262.6 200 110 262.6 200 90 262.6 200 100 262.6 200 120 262.6 400 120 462.6 400 140 462.6 400 150 462.6 400 180 462.6 400 150 462.6 600 240 662.6 600 200 662.6 600 250 662.6 600 250 662.6 600 210 662.6 800 280 862.6 800 320 862.6 800 300 862.6 800 300 862.6 800 300 862.6 1000 360 1062.6 1000 380 1062.6 1000 380 1062.6 1000 400 1062.6 1000 400 1062.6𝑺 = 𝟎.𝟑𝟔 ±𝟎.𝟎𝟏𝟑𝟗 𝑩 = −𝟔.𝟏𝟑𝟔 ± 𝟗.𝟗𝟗𝟔 𝑚𝑡= 𝑋 𝑚𝑠= 𝑌 So 𝒎𝒔= 𝑺 ∗𝒎𝒕 + b (y=mx + b) 𝐴𝑐𝑐𝑜𝑟𝑑𝑖𝑛𝑔 𝑡𝑜 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑎𝑛𝑢𝑎𝑙: 𝒎𝒔= 𝝁𝒌∗𝒎𝒕 and 𝜇𝑘 is the coefficient of friction Since: 𝑚𝑠= 𝑆 ∗𝑚𝑡 and 𝑚𝑠= 𝜇𝑘∗ 𝑚𝑡 Then 𝝁𝒌= 𝑺 𝛿𝜇𝑘= 𝛿𝑠= 0.0139 𝝁𝒌= 𝟎.𝟑𝟔 ± 𝟎.𝟎𝟏𝟑𝟗2) m (g) ms (g) mt (g) 100 120 226.7 100 120 226.7 100 120 226.7 100 140 226.7 100 100 226.7 200 200 326.7 200 200 326.7 200 200 326.7 200 180 326.7 200 220 326.7 300 260 426.7 300 240 426.7 300 280 426.7 300 240 426.7 300 260 426.7 400 300 526.7 400 300 526.7 400 320 526.7 400 340 526.7 400 340 526.7 500 380 626.7 500 340 626.7 500 360 626.7 500 360 626.7 500 360 626.7 Linest, S 0.6 -4.82 B δS 0.025133 11.29778 δB 𝝁𝒌= 𝑺 = 𝟎.𝟔 𝜹𝝁𝒌= 𝜹𝒔= 𝟎.𝟎𝟐𝟓𝟏 𝝁𝒌= 𝟎.𝟔±𝟎.𝟎𝟐𝟓𝟏3) L= 104 cm d= 16.3 cm m (g) mt (g) H (cm) y (cm) θ (rads) μk 200 262.6 34.7 18.4 0.177859 0.179759 400 462.6 35.7 19.4 0.187638 0.189871 600 662.6 38.3 22 0.213149 0.216436 800 862.6 37.9 21.6 0.209215 0.212322 1000 1062.6 42.4 26.1 0.253673 0.259259 Y= H-d Example: Y = 34.7 – 16.3 = 18.4 cm 𝐬𝐢𝐧(𝜽)=𝒚𝑳=𝑯−𝒅𝑳 𝒔𝒐 𝐚𝐫𝐜𝐬𝐢𝐧(𝒚𝑳) = 𝜽 Example: 𝜃 = arcsin(𝑦𝐿) = arcsin(18.4104) = arcsin(0.1769)= 0.1778 rads According to manual: μk = 𝐭𝐚𝐧 (𝜽) Example: μk = tan(𝜃)= 𝑡𝑎𝑛(0.1778)= 0.1796 𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝝁𝒌= ∑𝝁𝒌𝒏= 𝟎.𝟏𝟕𝟗𝟖+𝟎.𝟏𝟖𝟗𝟗+𝟎.𝟐𝟏𝟔𝟒+𝟎.𝟐𝟏𝟐𝟑+𝟎.𝟐𝟓𝟔𝟑𝟓= 𝟎.𝟐𝟏𝟏𝟓 Standard deviation found through excel: δ𝝁𝒌 = 0.030746 𝝁𝒌= 𝟎.𝟐𝟏𝟏𝟓 ±𝟎. 𝟎𝟑𝟎𝟕𝟓 4)Same equations as the ones used in question 3 m (g) mt (g) H (cm) y (cm) θ (rads) μk 200 326.7 45.3 29 0.282592 0.290363 400 526.7 49.4 33.1 0.323903 0.335727 600 726.7 45 28.7 0.27959 0.28711 800 926.7 45.2 28.9 0.281591 0.289278 1000 1126.7 47.4 31.1 0.303685 0.313378 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 μk = 0.303171 Standard deviation = 0.02109 𝝁𝒌= 𝟎.𝟑𝟎𝟑𝟐 ±𝟎.