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?
0.25 J
0.5 J
1 J
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.
