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?

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Q: 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?

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

Steps: 8

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.