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3. Would a measured force of (86.5±2.1)N be in agreement with a theoretically calculated force of (82.1±2.0)N? Show your work.

3. Would a measured force of (86.5±2.1)N be in agreement with a theoretically calculated force of (82.1±2.0)N? Show your work.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem 3:** Would a measured force of \( (86.5 \pm 2.1) \, \text{N} \) be in agreement with a theoretically calculated force of \( (82.1 \pm 2.0) \, \text{N} \)? Show your work. --- *Explanation:* To determine if the measured and theoretical forces are in agreement, we must check if the two values overlap within their uncertainty ranges. 1. **Measured Force:** - Value: \( 86.5 \, \text{N} \) - Uncertainty: \( \pm 2.1 \, \text{N} \) - Range: \( 86.5 - 2.1 \) to \( 86.5 + 2.1 \) - Range: \( 84.4 \, \text{N} \) to \( 88.6 \, \text{N} \) 2. **Theoretical Force:** - Value: \( 82.1 \, \text{N} \) - Uncertainty: \( \pm 2.0 \, \text{N} \) - Range: \( 82.1 - 2.0 \) to \( 82.1 + 2.0 \) - Range: \( 80.1 \, \text{N} \) to \( 84.1 \, \text{N} \) *Conclusion:* Check for overlap between the ranges: - Measured: \( 84.4 \) to \( 88.6 \, \text{N} \) - Theoretical: \( 80.1 \) to \( 84.1 \, \text{N} \) Since these ranges do not overlap, the measured force is not in agreement with the theoretically calculated force within the given uncertainties.
Transcribed Image Text:**Problem 3:** Would a measured force of \( (86.5 \pm 2.1) \, \text{N} \) be in agreement with a theoretically calculated force of \( (82.1 \pm 2.0) \, \text{N} \)? Show your work. --- *Explanation:* To determine if the measured and theoretical forces are in agreement, we must check if the two values overlap within their uncertainty ranges. 1. **Measured Force:** - Value: \( 86.5 \, \text{N} \) - Uncertainty: \( \pm 2.1 \, \text{N} \) - Range: \( 86.5 - 2.1 \) to \( 86.5 + 2.1 \) - Range: \( 84.4 \, \text{N} \) to \( 88.6 \, \text{N} \) 2. **Theoretical Force:** - Value: \( 82.1 \, \text{N} \) - Uncertainty: \( \pm 2.0 \, \text{N} \) - Range: \( 82.1 - 2.0 \) to \( 82.1 + 2.0 \) - Range: \( 80.1 \, \text{N} \) to \( 84.1 \, \text{N} \) *Conclusion:* Check for overlap between the ranges: - Measured: \( 84.4 \) to \( 88.6 \, \text{N} \) - Theoretical: \( 80.1 \) to \( 84.1 \, \text{N} \) Since these ranges do not overlap, the measured force is not in agreement with the theoretically calculated force within the given uncertainties.
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