Question

Find the uncertainty in kinetic energy. Kinetic energy depends on mass and velocity according to this function E(m,v) = 1/2 m v2. Your measured mass and velocity have the following uncertainties 0.37 kg and 0.42 m/s. What is is the uncertainty in energy, , if the measured mass, m = 1.06 kg and the measured velocity, v = -1.28 m/s? Units are not needed in your answer.

Answer 1

ΔK = 0.87296

Step-by-step explanation:

Given

m = 1.06 kg

Δm = 0.37 kg

v = - 1.28 m/s

Δv = 0.42 m/s

ΔK = ?

We apply the equation

ΔK = Δm*║∂K/∂m║ + Δv*║∂K/∂v║

⇒ ΔK = Δm*║v²/2║ + Δv*║m*v║

⇒ ΔK = (0.37)*║(- 1.28)²/2║ + (0.42)*║1.06*(- 1.28)║

⇒ ΔK = 0.87296