Calculate first-order combined standard uncertainty from uncorrelated mass and velocity measurements, or choose an inverse solve mode. This classical approximation is intended for small input uncertainties and does not provide a guaranteed error bound.

First-order combined standard uncertainty for uncorrelated mass and velocity measurements. Not a guaranteed error bound; small uncertainties and classical motion are assumed.

Related Calculators

Kinetic Energy Uncertainty Formula

The following formula is used to calculate the propagated uncertainty in kinetic energy for independent (uncorrelated) uncertainties in mass and velocity, using first-order uncertainty propagation for \(KE=\tfrac12 m v^2\).

ฮ” KE = โˆš((0.5 vยฒ ฮ” m)ยฒ + (m v ฮ” v)ยฒ)

Variables:

  • ฮ”KE is the uncertainty in kinetic energy
  • m is the mass
  • ฮ”v is the uncertainty in velocity
  • ฮ”m is the uncertainty in mass
  • v is the velocity

To calculate the uncertainty in kinetic energy, compute the sensitivity to each measurement (the partial derivatives with respect to m and v), multiply each by its uncertainty, square the results, add them, and then take the square root.

What is Kinetic Energy Uncertainty?

Kinetic energy uncertainty refers to the potential error or variation in the calculated kinetic energy of an object due to uncertainties in the measurements of its mass and velocity. In experimental physics and engineering, measurements are never perfectly accurate, and these uncertainties must be accounted for to provide a more accurate representation of the kinetic energy. Combined standard uncertainty estimates the standard deviation associated with the calculated energy under the measurement model. It is not a guaranteed range for the true value; coverage depends on the input distributions and adequacy of the first-order approximation.

How to Calculate Kinetic Energy Uncertainty?

The following steps outline how to calculate the Kinetic Energy Uncertainty.

  1. First, determine the mass (m) of the object.
  2. Next, determine the velocity (v) of the object.
  3. Next, determine the uncertainty in mass (ฮ”m).
  4. Next, determine the uncertainty in velocity (ฮ”v).
  5. Finally, calculate the uncertainty in kinetic energy using the formula \(\Delta KE = \sqrt{(0.5\,v^2\,\Delta m)^2 + (m\,v\,\Delta v)^2}\).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Mass (m) = 10 kg

Velocity (v) = 5 m/s

Uncertainty in Mass (ฮ”m) = 0.2 kg

Uncertainty in Velocity (ฮ”v) = 0.1 m/s