Question

QUESTION 2 Find the uncertainty in the moment of interia. Moment of interia of a disk depends on mass and radius according to this function (m,r) = 1/2 m 12. Your measured mass and radius have the following uncertainties Sm = 0.36 kg and Sr = 0.39 m. What is is the uncertainty in moment of interia, SI, if the measured mass, m = 3.18 kg and the measured radius, r = 2.13 m? Units are not needed in your answer. QUESTION 3 The propagation of uncertainty formula for the equation y = mx +b is ay Sm am ay SX ду where for example Sm is the uncertainty on m and is the partial derivative of y with respect to m. Ifm - -4.8 +/-0.7, X - 3.5+/-0.4 and b--2.8+/-0.7 then дт what is the uncertainty on y? QUESTION 4 Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function Eſm,v) = 1/2 m v2. Your measured mas s and velocity have the following uncertainties Sm = 0.4 kg and Sv = 0.24 m/s. What is is the uncertainty in energy, SE , if the measured mass, m = 7.34 kg and the measured velocity, V = -14.69 m/s? Units are not needed in your answer.

propagation of uncertainty

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Answer 1

Solution

2) 2.76498 (kgm^2)

3) 3.19044

4) 50.32280 (kgm^2/s^2)

4) Creven Ea śmur a) DE 22 and 3 Thus by uncertainly formula, SE = Iconset S ma 12+ Ce sv) om a) SE C 2 + (musu) 2 Substituting gevers values, (-14.69) ( 34 -1.621 624 + a) SEE 50.32280 tegns 2/2

y FS gewers by, Greven uncertainity in Sy - Jay 8m)2+ SD je to s b)2 we have y=mx+b as ay วิว ду ах m and ду -I ab Govern the values, ME -418 Sm=0.7 x 35 Sr=0.4 Sb=017 b = 2.8 > Thus Sy - Jox Sm ) + (68x)+(8632 √3.5*0.7²+ +-418*04)²+(017)2 Sy 3.19044 mr of om åre and af ar 2) Greven If ámra Thus by propagation of eronsor formula, SI = |(27 sm) 2+ DI so) =) Sia omy it (moss)2 2 Substituting gevens valves S1 -1(0.364.2.13%)2 + (3. 18 * 2.13x0.39)2 =) SI 2.76498 koma