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A speed of 30 m/s is measured with an uncertainty of ±0.5 m/s. What is the total

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Question: A speed of 30 m/s is measured with an uncertainty of ±0.5 m/s. What is the total uncertainty if this speed is used to calculate kinetic energy?

Options:

  1. 0.25 J
  2. 0.5 J
  3. 1 J
  4. 2 J

Correct Answer: 1 J

Solution: 

Kinetic energy = 0.5 * m * v²; uncertainty in KE = 2 * v * uncertainty in v = 2 * 30 * 0.5 = 30 J.

A speed of 30 m/s is measured with an uncertainty of ±0.5 m/s. What is the total

Practice Questions

Q1
A speed of 30 m/s is measured with an uncertainty of ±0.5 m/s. What is the total uncertainty if this speed is used to calculate kinetic energy?
  1. 0.25 J
  2. 0.5 J
  3. 1 J
  4. 2 J

Questions & Step-by-Step Solutions

A speed of 30 m/s is measured with an uncertainty of ±0.5 m/s. What is the total uncertainty if this speed is used to calculate kinetic energy?
  • Step 1: Understand the formula for kinetic energy, which is KE = 0.5 * m * v², where v is the speed.
  • Step 2: Identify the given speed, which is 30 m/s.
  • Step 3: Identify the uncertainty in the speed, which is ±0.5 m/s.
  • Step 4: Recognize that the uncertainty in kinetic energy (KE) can be calculated using the formula: uncertainty in KE = 2 * v * uncertainty in v.
  • Step 5: Substitute the values into the formula: v = 30 m/s and uncertainty in v = 0.5 m/s.
  • Step 6: Calculate the uncertainty in KE: uncertainty in KE = 2 * 30 * 0.5.
  • Step 7: Perform the multiplication: 2 * 30 = 60, then 60 * 0.5 = 30.
  • Step 8: Conclude that the total uncertainty in kinetic energy is 30 J.
  • Kinetic Energy Calculation – Understanding how to calculate kinetic energy using the formula KE = 0.5 * m * v² and how to propagate uncertainty in measurements.
  • Uncertainty Propagation – Applying the rules of uncertainty propagation, particularly for functions of measured quantities, to determine the total uncertainty in derived quantities.
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