Enter the mass, velocity, uncertainty in mass, and uncertainty in velocity into the calculator to determine the propagated uncertainty in kinetic energy.
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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 \(KE=\tfrac12 m v^2\).
\Delta KE = \sqrt{\left(0.5\,v^2\,\Delta m\right)^2 + \left(m\,v\,\Delta v\right)^2}Variables:
- ΔKE is the uncertainty in kinetic energy
- m is the mass
- Δv is the uncertainty in velocity
- Δm 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. The uncertainty in kinetic energy helps in understanding the range within which the true value of kinetic energy lies, considering the possible errors in the measurements of mass and velocity.
How to Calculate Kinetic Energy Uncertainty?
The following steps outline how to calculate the Kinetic Energy Uncertainty.
- First, determine the mass (m) of the object.
- Next, determine the velocity (v) of the object.
- Next, determine the uncertainty in mass (Δm).
- Next, determine the uncertainty in velocity (Δv).
- Finally, calculate the uncertainty in kinetic energy using the formula \(\Delta KE = \sqrt{(0.5\,v^2\,\Delta m)^2 + (m\,v\,\Delta v)^2}\).
- 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 (Δm) = 0.2 kg
Uncertainty in Velocity (Δv) = 0.1 m/s