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A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. If this speed is

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Question: A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. If this speed is used to calculate kinetic energy, what is the percentage error in kinetic energy?

Options:

  1. 5%
  2. 2.5%
  3. 1%
  4. 10%

Correct Answer: 2.5%

Solution: 

K.E. = 0.5 * m * v², percentage error = 2 * (Δv/v) = 2 * (0.5/20) = 0.05 or 5%.

A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. If this speed is

Practice Questions

Q1
A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. If this speed is used to calculate kinetic energy, what is the percentage error in kinetic energy?
  1. 5%
  2. 2.5%
  3. 1%
  4. 10%

Questions & Step-by-Step Solutions

A speed is measured as 20 m/s with an uncertainty of ±0.5 m/s. If this speed is used to calculate kinetic energy, what is the percentage error in kinetic energy?
  • Step 1: Understand the formula for kinetic energy (K.E.). The formula is K.E. = 0.5 * m * v², where 'm' is mass and 'v' is speed.
  • Step 2: Identify the given speed (v) and its uncertainty (Δv). Here, v = 20 m/s and Δv = ±0.5 m/s.
  • Step 3: Calculate the relative uncertainty in speed. This is done by dividing the uncertainty by the measured speed: Δv/v = 0.5 m/s / 20 m/s.
  • Step 4: Perform the division: 0.5 / 20 = 0.025.
  • Step 5: To find the percentage error in kinetic energy, multiply the relative uncertainty by 2 (because kinetic energy depends on the square of speed): percentage error = 2 * (Δv/v).
  • Step 6: Calculate the percentage error: 2 * 0.025 = 0.05.
  • Step 7: Convert the decimal to a percentage: 0.05 = 5%.
  • Kinetic Energy Calculation – Understanding the formula for kinetic energy (K.E. = 0.5 * m * v²) and how to apply it to find the effect of uncertainty in velocity on kinetic energy.
  • Propagation of Uncertainty – Applying the concept of uncertainty propagation to determine how the uncertainty in velocity affects the calculated kinetic energy.
  • Percentage Error – Calculating percentage error based on the relative uncertainty in the measured quantity.
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