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?
5%
2.5%
1%
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 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.
