Length and Value of KE Question. Please Check Answer

[cbrowne]

Homework Statement

1) Two pieces of wood are glued together to form a long stick. The length of the
first piece is L1 = 0.97 ± 0.02 m, and the length of the second piece is
L2 =1.04 ± 0.01 m. What is the length (including uncertainty) of the stick?

2) An object of mass m = 2.3± 0.1 kg , is moving at a speed of
v =1.25 ± 0.03 m/s . Calculate the kinetic energy ( KE = 1/2 mv2 ) of the object.
What is the uncertainty in the calculated value of KE ?



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L₁+L₂ = .97 + 1.04 ± Δuncertainty
Δu = sqrt(u12 + u22 + ...) = √ (.02^2+.01^2) =.0224
L₁+L₂ = 2.01 ± 0.0224m
KE=0.5mv2 ± Δ u= 1.80±Δ


Δu=dX/X = sqrt( (dA/A)2 + (dB/B)2 +...) =
=dX/1.80 = sqrt( (0.1/2.3)2 + (0.03/1.25)2 )
=√.002466*1.80
=.0853
KE=1.80±.0853J

 

[LowlyPion]

Giving your uncertainty with more significant digits than the precision of results is not exactly the best way to handle it in 1).

In 2) you need to add the square of the relative uncertainties of the V twice to account for the V² and then add the square of the m uncertainty and then take the square root.

 

[thomate1]

In both cases, the uncertainty is calculated using the root sum square method, taking into account the uncertainties in the individual measurements. The length of the stick is 2.01 ± 0.0224m, and the kinetic energy of the object is 1.80 ± 0.0853J. These uncertainties reflect the precision and accuracy of the measurements and should be considered when interpreting the results.