Question

plane is roughly level. Lay the spirit level across the two rails and level them using the levelling feet. Now put the spirit level along one rail and adjust the support rod to 2. 3. level the rail. se on the rails at the support rod end and mark its position. Then make similar mark 1.2 meters along the rail. easure up from the bench to the underside of the front rail at each mark and record the heights a, and be (Note the position of side 'd and 'b' in Figure 1) 6. The table may not be exactly flat, find the height difference error ay,and record it in Table 1.0 7. Now raise the rails about a 40 mm at side'a. Place the larger disc on the high end of the rails (side and line up the axle perpendicular to the rails, holding it while preparing to use the stopwatch. Measure the time taken for the released disc to roll tself 1.2 m down the inclined rails. Repeat the same measurement to obtain the second reading. Record the results Repeat (8) using the smaller disc, recording the results in Table 1. 8. 9. Now raise the rails about a further 40 mm and repeat the height and time measurements (8 and 9). 10. Repeat this twice more, obtaining four sets of readings altogether of times and heights. TABLE 1 bo (mm) Ay。(mm) 28 36 2 TABLE 2 队 Rolling times Inclination of rails Mass3.34s k Messs 368k Higher Lower end H-la-bJ-by. Log H end b(mm) (mm) aN (mm) Smaller disc Height Larger disc ve Log t 68 55 5 63 16구6 2 108 7 9.45 9.1s 7-54 1-42 148 96 759 646 6.4S 188 S 1.73 9-66 1. Use the Excel software or plot manually graph (log t) vs (log H) for the large and small disc on the same axis. 2. Draw the lines of the best fit 3. Find y-intercept for each line (c) 4. Calculate k as antilog of 2c (k 10c) 5. Show calculations of the moment of inertia for each disc using expression (7) Record the result in the Table 3. 6. Large Disc- Ma ss = Small Disc: Mass= TABLE 3 Moment of Inertia Line of the best fit I (kg mm2) mxtc Large Disc Small Disc

Answer 1

solution: Table 1:

a0(mm)	b0(mm)	$\Delta$y0(mm)
28	36	-8

Table-2:

Inclination of rails

Rolling times

	higher end aN(mm)	lower end bN(mm)	height H=(aN-bN)-$\Delta$y0(mm)	log H			larger disc		smaller disc
					t1 t2	taverage	log t	t1 t2	taverage	log t
1	68	55	21	1.3222	25.63 25.45	25.54	1.4072	16.49 16.76	16.625	1.2206
2	108	74	42	1.6232	14.95 14.77	14.86	1.1720	9.45 9.75	9.60	0.9823
3	148	96	60	1.7782	11.62 11.51	11.56	1.0630	7.54 7.59	7.565	0.8785
4	188	115	81	1.9085	9.73 9.66	9.695	0.9863	6.46 6.45	6.455	0.8098

Graph between log t vs log H

for larger disc

for large disc 2.0 1.9 yaa+ bx Equation 1.8 No Weightng 324908 t0.0837 137499 t0.05454 Slope Sumof Squares 599574-4 0.99843 099888 1.7 Peason'sr R-Square(COD 0.9953 1.6. 1.5 1.3 1.1 1.0 1.2 1.3 1.4 log t

for smaller disc

for smaller disc 2.0 Equation log H No Weightng Plot Weight 3.01963t0.07824 ntercept 139388 +007941 Slope 0.001 Resdual Sumof Squares 09888 Pearson'sr 0.9938 R-Square R-SquaE 0.9904 o 1.6 0.8 0.9 log t

Table 3:

	line of the best fit y=mx+c	c	k (mm)	moment of inertia I(kg mm2) I=Mk2
large disc M=3.345 kg	y=-1.3749x+3.2490	3.2490	3.1477*106	33.1423*1012
small disc M=1.368 kg	y=-1.3996x+3.0196	3.0196	1.0945*106	1.638*1012