To calculate the maximum uncertainty of kinetic energy, we need to consider the propagation of uncertainties using the formula for kinetic energy.
The formula for kinetic energy is:
KE = (1/2) * m * v^2
where: KE is the kinetic energy, m is the mass, and v is the velocity.
To calculate the maximum uncertainty of kinetic energy, we will consider the percentage uncertainties in mass and velocity. Let's assume the mass uncertainty is 2% and the velocity uncertainty is 3%.
First, we calculate the individual contributions of mass and velocity uncertainties to the uncertainty in kinetic energy.
Uncertainty in mass (Δm) = (2/100) * m Uncertainty in velocity (Δv) = (3/100) * v
Next, we use the following formula to calculate the overall uncertainty in kinetic energy (ΔKE) using the percentage uncertainties:
ΔKE = sqrt((Δm/m)^2 + (2 * Δv/v)^2) * KE
Let's substitute the values into the formula:
ΔKE = sqrt((Δm/m)^2 + (2 * Δv/v)^2) * KE = sqrt((2/100)^2 + (2 * 3/100)^2) * KE = sqrt((0.02)^2 + (2 * 0.03)^2) * KE = sqrt(0.0004 + 0.0018) * KE = sqrt(0.0022) * KE ≈ 0.047 * KE
Therefore, the maximum uncertainty of kinetic energy is approximately 0.047 times the value of kinetic energy.
Note: This calculation assumes that the uncertainties in mass and velocity are independent and that they follow a normal distribution.