question 3 **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.

The measured force is 86.5±2.1 N. The theoretically calculated force is 82.1±2.0 N.

Answered: 3. Would a measured force of…

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

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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Question

question 3

**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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