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Questions and Answers
What is the relative uncertainty of a measurement of 25.0 cm ± 0.5 cm?
What is the relative uncertainty of a measurement of 25.0 cm ± 0.5 cm?
- 2.0
- 0.02 (correct)
- 0.05
- 0.2
Which formula is used to calculate the uncertainty in a reciprocal, like when finding the frequency from the period measurement?
Which formula is used to calculate the uncertainty in a reciprocal, like when finding the frequency from the period measurement?
- $\frac{\Delta f}{T} = \frac{\Delta T}{f}$
- $\frac{\Delta f}{f} = \frac{\Delta T}{T}$ (correct)
- $\Delta f = \Delta T - f$
- $\Delta f = \frac{\Delta T}{T} + f$
If the period of a pendulum is measured as 1.50 s ± 0.03 s, what is the absolute uncertainty in the frequency calculated using the equation f = 1/T?
If the period of a pendulum is measured as 1.50 s ± 0.03 s, what is the absolute uncertainty in the frequency calculated using the equation f = 1/T?
- 0.04 Hz
- 0.03 Hz
- 0.01 Hz
- 0.02 Hz (correct)
Why is it important to consider uncertainty in measurements and calculations?
Why is it important to consider uncertainty in measurements and calculations?
Flashcards
Uncertainty
Uncertainty
The measure of doubt in a measurement; indicates reliability.
Absolute Uncertainty
Absolute Uncertainty
The exact amount of uncertainty in a measurement; same units as the measurement.
Relative Uncertainty
Relative Uncertainty
Compares absolute uncertainty to measured value; expressed as fraction or percentage.
Propagation of Uncertainty
Propagation of Uncertainty
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Uncertainty in Reciprocals
Uncertainty in Reciprocals
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Study Notes
Uncertainty in Measurements
- Uncertainty quantifies the doubt in a measurement, indicating data reliability.
Absolute Uncertainty
- Absolute uncertainty is the numerical difference from the actual value of the measurement.
- It has the same units as the measurement itself.
- Example: 50.0 cm ± 0.2 cm, the 0.2 cm value is the absolute uncertainty.
Relative Uncertainty
- Relative uncertainty expresses uncertainty as a fraction or percentage of the measured value.
- Formula: Relative Uncertainty = (Absolute Uncertainty / Measured Value)
- Example: For 50.0 cm ± 0.2 cm, the relative uncertainty is 0.2 cm / 50.0 cm = 0.004 (or 0.4%). This signifies the uncertainty is 0.4% of the total length.
Propagation of Uncertainty
- Uncertainty propagates through calculations involving multiple measurements.
- Example: Calculating pendulum frequency from period measurement.
Example: Pendulum Period and Frequency
- Pendulum period: 2.00 s ± 0.05 s
- Frequency (f) calculation: f = 1/T = 1/2.00 s = 0.500 Hz
- To find uncertainty in frequency:
- Formula for uncertainty in reciprocals: Δf/f = ΔT/T
- Calculation: Δf/0.500 = 0.05 s / 2.00 s = 0.025
- Final result: Δf = 0.0125 Hz ≈ 0.01 Hz.
- Thus, the frequency is 0.500 ± 0.01 Hz.
- This illustrates the impact of uncertainty on calculations.
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