very difficult question on error analysis, please help...?

Question

You check conservation of the total mechanical energy by comparing the change in potential energy of the mass m with the change in kinetic energy, delta dKE, of the masses m and M combined, which is 340grams . The change in kinetic energy is dKE = 1/2(m+M)v2 (see Ch6 sheet 8), where v is the velocity of the glider when starting with zero initial velocity, v = 0.5 m/s. In your error calculations you have previously determined the error of the term [ 1/2(m+M) ] to be 1.138%, and the relative error of the velocity v to be 0.00855. What is the absolute error of dKE ?

the answer is .000873 but i need to understand how to get it, please help

Answer 1

Ok, you need to know this :

(x +/- dx)(y +/- dy) = x*y +/- (x*dy + y*dx)

M+m = 340 grams = 340*10^-3 kg

v = 0.5 m/s

(1/2(M+m) +/- dm) = 170*10^-3 +/- 1.93*10^-3

(v +/- dv) = 0.5 +/- 0.00855

(v +/- dv)^2 = 0.25 +/- 8.55*10^-3

(170*10^-3 +/- 1.93*10^-3)*(0.25 +/- 8.55*10^-3) =

( 42.5*10^-3 +/- 1.453*10^-3+ 4.825*10^-4)

then : the error will be : 1.453*10^-3+ 4.825*10^-4

That will be : 0.00193

I got that, maybe something was wrong, I'll check it later ok.