Math Problem Statement

Compare your theoretical value (from part 0.3) to the calculated value by percent error? Describe two physical reasons that could cause the discrepancy.

Solution

In the image, you are calculating the percent error between a theoretical and a calculated value, then discussing possible reasons for the discrepancy.

The calculation for percent error is: Percent Error=Experimental ValueTheoretical ValueTheoretical Value×100\text{Percent Error} = \frac{\left| \text{Experimental Value} - \text{Theoretical Value} \right|}{\text{Theoretical Value}} \times 100 In your case: Percent Error=0.00630.3750.375×100=98.32%\text{Percent Error} = \frac{|0.0063 - 0.375|}{0.375} \times 100 = 98.32\% This shows a very large percent error.

The reasons for this discrepancy, as written, include:

  1. Assumption that the pulley doesn't have rotational inertia: This means the pulley is assumed to not resist changes in rotational motion, which could cause errors in the calculated forces or accelerations.
  2. Neglecting the weight of the string: If the string has mass, its weight would affect the overall forces in the system, leading to a discrepancy in theoretical calculations.

Would you like more details on this calculation or the physical interpretations?

Here are some follow-up questions:

  1. What other physical factors could affect the experiment's outcome?
  2. How does rotational inertia influence pulley systems?
  3. What is the role of friction in pulley systems, and how might it affect results?
  4. Could air resistance affect this experiment significantly?
  5. How can the theoretical model be improved to account for the discrepancies?

Tip: Always check if assumptions made in theoretical models hold true in real-world conditions, as they can lead to significant percent errors.

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Math Problem Analysis

Mathematical Concepts

Percent Error
Absolute Value
Ratios

Formulas

Percent Error = (|Experimental Value - Theoretical Value| / Theoretical Value) * 100

Theorems

Error Analysis

Suitable Grade Level

Grades 9-12