VI 1 Nylon Ball d cm 26 5 26 5 26 5 26 5 26 5 30 4 30 4 30 4 30 4 30 4 35 7 35 7 35 7 35 7 35 7 40 5 40 5 40 5 40 5 40 5 46 4 46 4 46 4 46 4 46 4 51 2 51 2 51 2 51 2 51 2 y cm 13 3 13 3 13 3 13 3 13 3 17 4 17 4 17 4 17 4 17 4 22 6 22 6 22 6 22 6 22 6 27 4 27 4 27 4 27 4 27 4 33 1 33 1 33 1 33 1 33 1 38 3 38 3 38 3 38 3 38 3 t s t2 s2 0 1629 0 0265 0 1629 0 0265 0 1629 0 0265 0 1629 0 0265 0 1629 0 0265 0 1858 0 0345 0 1855 0 0344 0 1859 0 0346 0 1853 0 0343 0 1857 0 0345 0 214 0 0458 0 2138 0 0457 0 214 0 0458 0 214 0 0458 0 2137 0 0457 0 235 0 0552 0 2505 0 0628 0 2406 0 0579 0 2392 0 0572 0 2358 0 0556 0 2658 0 0706 0 2675 0 0716 0 2644 0 0699 0 2599 0 0675 0 263 0 0692 0 2851 0 0813 0 2852 0 0813 0 2862 0 0819 0 2831 0 0801 0 2825 0 0798 To find t 2 s2 0 16292 0 1629 0 1629 0 0265 s2 y cm 13 3 13 3 13 3 13 3 13 3 17 4 17 4 17 4 17 4 17 4 22 6 22 6 22 6 22 6 22 6 27 4 27 4 27 4 27 4 27 4 33 1 33 1 33 1 33 1 33 1 38 3 38 3 38 3 38 3 38 3 t s t2 s2 0 1634 0 0267 0 1637 0 0268 0 1636 0 0268 0 1639 0 0269 0 1629 0 0265 0 1859 0 0346 0 186 0 0346 0 1864 0 0347 0 1864 0 0347 0 1863 0 0347 0 2137 0 0457 0 0458 0 214 0 214 0 0458 0 2132 0 0455 0 2141 0 0458 0 2354 0 0554 0 2347 0 0551 0 2357 0 0556 0 2349 0 0552 0 235 0 0552 0 2594 0 0673 0 2588 0 0670 0 2594 0 0673 0 2599 0 0675 0 2598 0 0675 0 2783 0 0775 0 2787 0 0777 0 2789 0 0778 0 2789 0 0778 0 2789 0 0778 Steel Ball d cm 26 5 26 5 26 5 26 5 26 5 30 4 30 4 30 4 30 4 30 4 35 7 35 7 35 7 35 7 35 7 40 5 40 5 40 5 40 5 40 5 46 4 46 4 46 4 46 4 46 4 51 2 51 2 51 2 51 2 51 2 VI 2 The same calculation is carried out to find t2 s2 as carried out in the table of the nylon ball Nylon Ball y cm 13 3 13 3 13 3 13 3 13 3 17 4 17 4 17 4 17 4 17 4 22 6 22 6 22 6 22 6 22 6 27 4 27 4 27 4 27 4 27 4 33 1 33 1 33 1 33 1 33 1 38 3 38 3 38 3 38 3 38 3 slope t2 s2 0 0265 0 0263 0 0266 0 0267 0 0266 0 0345 0 0344 0 0346 0 0343 0 0345 0 0458 0 0457 0 0458 0 0458 0 0457 0 0552 0 0628 0 0579 0 0572 0 0556 0 0706 0 0716 0 0699 0 0675 0 0692 0 0813 0 0813 0 0819 0 0801 0 0798 slope unc 451 48839 6 1872380 1 1 63450798 0 34579141 intercept unc intercept 0 0300 0 0400 0 0500 0 0600 0 0700 0 0800 0 0900 t2 s2 y vs t2 Nylon Ball f x 451 49 x 1 63 m c y 45 40 35 30 25 20 15 10 5 0 0 0200 Slope given through Excel 451 48839 cm s2 Y intercept given through Excel 1 63450798 Uncertainty of slope 6 18723801 To calculate the value of g we use the equation y gt2 2 t2 y t2 g 2 t 2 So we have Here t 2 would cancel out on the right hand side This would then leave us with y t2 g 2 y t2 would be replaced with the value of the slope given in excel Solving for g s g 2 Where s 451 49 cm s2 We now have 2 451 49 g 2 2 where 2 would cancel on the right side of the equation We multiply 2 by value of s to get the value of g We use the equation s s 2 After simplifying we get g g s s g g Now we can solve to get g 6 1872 451 49 g 902 98 Divide the left hand side to get 0 013704 Now multiply both sides by 902 98 to get the value of g g 902 98 0 013704 12 374 cm s2 So g g 903 12cm s2 Steel Ball g 902 98 cm s2 Solving for g y cm 13 3 13 3 13 3 13 3 13 3 17 4 17 4 17 4 17 4 17 4 22 6 22 6 22 6 22 6 22 6 27 4 27 4 27 4 27 4 27 4 33 1 33 1 33 1 33 1 33 1 38 3 38 3 38 3 38 3 38 3 Slope Slope Unc t2 s2 0 0267 0 0268 0 0268 0 0269 0 0265 0 0346 0 0346 0 0347 0 0347 0 0347 0 0457 0 0458 0 0458 0 0455 0 0458 0 0554 0 0551 0 0556 0 0552 0 0552 0 0673 0 0670 0 0673 0 0675 0 0675 0 0775 0 0777 0 0778 0 0778 0 0778 487 982 698 203 1 19491 0 06477 0 34739 058 544 Intercept Intercept Unc y vs t2 Steel Ball f x 487 98 x 0 35 m c y 45 40 35 30 25 20 15 10 5 0 0 0200 0 0300 0 0400 0 0500 0 0600 0 0700 0 0800 0 0900 t2 s2 Slope given through Excel 487 982698 cm s2 y intercept given through Excel 0 34739058 Calculated values using LINEST function in Excel Uncertainty of slope 1 19491203cm s2 So for the steel ball The calculations to find g and g are carried out the same way as with the previous data g 975 96 cm s2 g 2 3898 cm s2 g g 976 2cm s2 The calculated value of g for both the nylon ball and steel ball somewhat agrees with each other given that both values are above 900 when …