Physics Lab (Centripetal force) Question: Make a connection between the terms in

Question

Physics Lab (Centripetal force) Question:

Make a connection between the terms in the theoretical and trendline equations to find the experimental value of the 3-hooked mass (m).

Our data

Given -

What we need to find - Experimental mass = ?g

Make a connection between the terms in the theoretical and trendline equations to find the experimental value of the 3-hooked mass (m).

Our Data

Given-

Experimental mass = ?g

DATA TABLE #1: FIXED RADIUS MEASUREMENTS RADIUS r ± r cm | 16.0±0.05cm HANGING MASS MEAN ANGULAR SPEED STANDARD DEVIATION Wav L17 (rad/s) 2.28 2.59 3.17 3.46 (rad/s) 10.2 ± 0.05 20.0 ± 0.05 30.2 ± 0.05 40.0 ± 0.05 00.1.3 0.13 0.10

Explanation / Answer

FOr data table 1,
the trendline is y = 4.12x - 9.88
also, by pluggin in values fromk the table, we can see, x denotes mass, and y denotes w^2 ( angular velocity squared)

also, mr/g = slope of curve
hence, m = 4.12*g/r = 4.12*9.81/0.16 ( r = 16 +- 0.05 cm)
m = 252.6075
and dm/m = dr/r
so, dm = 0.05*252.6075/16 = 0.789
so, m = 252.6075 +- 0.789 kg

for table 2, similiar to table 1, we can see that slope of trendline is Mg/m
so, Mg/m = 224
but, M = 40+-0.05 kg
so, m = 40*9.81/224 = 1.7517 kg
and, dm/m = dM/M
dm = 0.05*1.7517/40 = 0.002

so, m = 1.7517 +- 0.002 kg

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