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In a physics experiment, the speed of an object is measured as 20.0 m/s with an

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Question: In a physics experiment, the speed of an object is measured as 20.0 m/s with an uncertainty of ±0.4 m/s. What is the maximum possible error in the kinetic energy calculated from this speed?

Options:

  1. 8 J
  2. 4 J
  3. 2 J
  4. 1 J

Correct Answer: 8 J

Solution: 

Kinetic energy = 0.5 * m * v²; maximum error = m * v * uncertainty in v = m * 20.0 * 0.4 = 8 J (assuming m = 1 kg).

In a physics experiment, the speed of an object is measured as 20.0 m/s with an

Practice Questions

Q1
In a physics experiment, the speed of an object is measured as 20.0 m/s with an uncertainty of ±0.4 m/s. What is the maximum possible error in the kinetic energy calculated from this speed?
  1. 8 J
  2. 4 J
  3. 2 J
  4. 1 J

Questions & Step-by-Step Solutions

In a physics experiment, the speed of an object is measured as 20.0 m/s with an uncertainty of ±0.4 m/s. What is the maximum possible error in the kinetic energy calculated from this speed?
  • Step 1: Understand the formula for kinetic energy, which is KE = 0.5 * m * v², where KE is kinetic energy, m is mass, and v is speed.
  • Step 2: Identify the given values: speed (v) = 20.0 m/s and uncertainty in speed = ±0.4 m/s.
  • Step 3: Recognize that the uncertainty in speed affects the kinetic energy calculation.
  • Step 4: Calculate the maximum possible error in kinetic energy using the formula: maximum error = m * v * uncertainty in v.
  • Step 5: Assume a mass (m) of 1 kg for simplicity in calculation.
  • Step 6: Substitute the values into the formula: maximum error = 1 kg * 20.0 m/s * 0.4 m/s.
  • Step 7: Perform the multiplication: 1 * 20.0 * 0.4 = 8 J.
  • Step 8: Conclude that the maximum possible error in the kinetic energy is 8 J.
  • Kinetic Energy Calculation – Understanding the formula for kinetic energy (KE = 0.5 * m * v²) and how to apply it to find maximum error based on speed uncertainty.
  • Propagation of Uncertainty – Applying the concept of uncertainty propagation to determine how the uncertainty in speed affects the calculated kinetic energy.
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