Combining Multiple Rules for Error Propagation

[ELLE_AW]

Homework Statement

1. An object of mass m=2.3±0.1kg moves at a speed of v=1.25±0.03m/s. Calculate the kinetic energy (K=1/2mv2) of the object and estimate the uncertainty δK?

Homework Equations

- Addition error propagation--> z = x + y and the Limit error--> δz = δx + δy

- Exponent error propagation --> z = xn and the Limit Error --> δz = nx^n-1(δx)

- K = 1/2mv²

The Attempt at a Solution

This is what I attempted, but I really don't think it's right. I basically just included the exponent error propagation, but how does the multiplication of mv² get incorporated?

- K = ½ mv2 = ½ (2.3kg)(1.25m/s)² = 1.7969 kg m² s^-2 = 1.8 J

- Uncertainty of K = (m)2v¹(δv) = (2.3)(2)(1.25)(0.03) = 0.1725 = 0.17
How do I combine these two rules when calculating the uncertainty of the kinetic energy?

 

[haruspex]

Relevant equations

You seem to be missing the product rule:
If z=xy then δz/z=δx/x+δy/y

 

[Orodruin]

Addition error propagation--> z = x + y and the Limit error--> δz = δx + δy

This is error propagation for correlated variables x and y. If your variables are uncorrelated, they should be added in quadrature, i.e.,
$$
\delta z^2 = \delta x^2 + \delta y^2.
$$
The same is true for uncorrelated relative errors in the case of a product.

 

[ELLE_AW]

Got it, thank you!