Help!! For a function of several variables, f = /(a,b,c,...), the propagation er

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Help!!

For a function of several variables, f = /(a,b,c,...), the propagation error in a measurement of f is sigma2f = ( f/ a2) sigma2a + ( f/ b) sigma2b + ( f/ c) sigma2c +... In your next lab, you will be introduced to the concept of kinetic energy, Kinetic Energy = K = 1/2mv2 where m is the mass of the object and v is its speed having the following values: m = 4.7 plusminus 0.5 kg v = 0.4 plusminus 0.2 m/sec Using the method of propagation errors, what is the kinetic energy and its uncertainty? Make certain you carefully show all your work.

Explanation / Answer

K = m*v^2/2 = 4.7*0.4^2/2 =0.376 Joules

dK = (dK/dm)*dm + (dK/dv)*dv

dK^2 = (dk/dm)^2*(dm^2) + (dK/dv)^2*(dv^2)

dk/dm = (1/2)v^2 =0.5*0.4 =0.2

dk/dv = mv = 4.7*0.4 =1.88

dm =0.5 kg

dv =0.2 m/s

(dk)^2 = 0.2^2 * dm^2 +1.88^2*dv^2 =0.04*0.25 +3.5344*0.04 =0.151376

dk = sqrt(dk^2) =0.38907 J

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