2021 AP Physics 1 Free Response #2 (First Administration)

Allen Tsao The STEM Coach
7 May 202109:18
EducationalLearning
32 Likes 10 Comments

TLDRIn this educational video, students explore the relationship between the thickness of a plastic rod and its maximum breaking force. Two models are discussed: one where force is directly proportional to the rod's radius, and another where it's proportional to the cross-sectional area. An experimental procedure is designed to test these hypotheses using rods of varying thicknesses, a ruler for measurements, and a spring scale to apply force until breakage. The results suggest a quadratic relationship, favoring Student B's model, as data points indicate that force increases with the square of the rod's radius.

Takeaways
  • πŸ” The students are investigating how the thickness of a plastic rod affects the maximum force it can withstand before breaking.
  • πŸ€” Two models are proposed: Student A suggests a direct proportionality between maximum force and the rod's radius, while Student B suggests a direct proportionality with the rod's cross-sectional area.
  • πŸ“ The experiment requires measuring the radius of the rods using a ruler and calculating the cross-sectional area using the formula \( \pi r^2 \).
  • πŸ“ˆ The force applied to the rods until breakage is measured using a spring scale.
  • 🧩 The rods are of the same material and length but vary in thickness.
  • πŸ”¨ The experimental procedure involves measuring the radius of the rods, attaching them to a fixed point, and pulling with a spring scale until they break.
  • πŸ“Ή It's suggested to record the force measurement with a video to capture the exact moment of breakage for verification.
  • πŸ“ˆ Student A's model predicts a linear relationship between the radius and the maximum force, while Student B's model predicts a quadratic relationship.
  • πŸ“Š The data provided in the script suggests a quadratic relationship, which aligns more with Student B's model.
  • πŸ“‰ The graph for Student A's model would be a straight line with no y-intercept, whereas Student B's model would show a curve representing a quadratic relationship.
  • πŸ“ The final analysis of the data points plotted on the graph indicates that the relationship between force and radius is more quadratic than linear, supporting Student B's model.
Q & A
  • What is the main objective of the students' investigation?

    -The main objective is to determine how the thickness of a plastic rod affects the maximum force it can withstand before breaking.

  • What are the two models proposed by the students to explain the relationship between the rod's thickness and the maximum force it can withstand?

    -Student A claims that the maximum force (Fmax) is directly proportional to the radius of the rod, while Student B claims that Fmax is directly proportional to the cross-sectional area of the rod.

  • What quantities need to be measured in the experiment?

    -The radius of the rod (r) and the force applied until the rod breaks (F).

  • What equipment is suggested for measuring the radius of the rod?

    -A meter stick or a ruler.

  • How is the force applied to the rod measured?

    -Using a spring scale.

  • Describe the overall procedure for the experiment.

    -1. Measure the radius of all the rods. 2. Attach one end of the rod to a fixed point. 3. Attach the other end of the rod to a spring scale. 4. Pull on the spring scale slowly and record the force until the rod breaks. 5. Repeat the procedure with all rods.

  • How is the data from the experiment used to determine which student's model is correct?

    -The data is plotted on a graph, with the rod's radius on the x-axis and the maximum force on the y-axis. The shape of the curve is analyzed to see if it matches a linear relationship (supporting Student A's model) or a quadratic relationship (supporting Student B's model).

  • What would a linear relationship between the rod's radius and the maximum force indicate?

    -It would indicate that the maximum force is directly proportional to the rod's radius, supporting Student A's model.

  • What would a quadratic relationship between the rod's radius and the maximum force indicate?

    -It would indicate that the maximum force is directly proportional to the cross-sectional area of the rod, supporting Student B's model.

  • Based on the provided data points, which student's model is supported by the experiment?

    -The data points suggest a quadratic relationship between the rod's radius and the maximum force, supporting Student B's model.

  • Why might a video recording be useful in this experiment?

    -A video recording with a clear shot of the spring scale measurement would be useful to accurately capture the force at the moment the rod breaks, as the reading may not be visible once the rod has broken.

Outlines
00:00
πŸ” Experimental Design to Test Rod Strength Models

This paragraph outlines an experiment to determine how the maximum force (f_max) a plastic rod can withstand before breaking is related to its thickness. The students are considering two models: one where f_max is directly proportional to the rod's radius (Student A's model), and another where it's proportional to the rod's cross-sectional area (Student B's model). The experiment involves measuring the radius of various rods, attaching one end to a fixed point and the other to a spring scale, and then pulling until the rod breaks while recording the force applied. The equipment required includes a ruler for measuring the radius and a spring scale for measuring the force. The procedure also suggests video recording the force measurement as the rod breaks to ensure accuracy in data collection.

05:02
πŸ“Š Data Analysis and Graph Representation of Rod Strength Models

The second paragraph discusses the analysis of the experimental data and the representation of the results on a graph. It involves plotting the relationship between the rod's radius (r) and the maximum force (f_max) it can withstand, according to the two proposed models. Student A's model suggests a linear relationship, while Student B's model indicates a quadratic one. The paragraph provides instructions for graphing these relationships, labeling them distinctly as 'A' or 'B'. It also includes a table with hypothetical data points for different rod radii and corresponding forces, which are then plotted on a graph to visually determine which model (linear or quadratic) better fits the data. The visual analysis suggests that the relationship is more quadratic than linear, thus favoring Student B's model.

Mindmap
Keywords
πŸ’‘Maximum Force (F_max)
F_max represents the maximum force that a plastic rod can withstand before breaking. In the video, it is used to compare different rods' strength based on their thickness, central to the experimental procedure discussed by the students.
πŸ’‘Rod Thickness
Rod thickness refers to the diameter or radius of the plastic rods being tested. The video explores how this variable affects the maximum force the rods can handle, with two students proposing different models to explain this relationship.
πŸ’‘Cross-Sectional Area
The cross-sectional area is the area of the circle formed by slicing through the rod perpendicular to its length. Student B claims that F_max is directly proportional to this area, highlighting its importance in determining the rod's strength.
πŸ’‘Proportionality
Proportionality refers to the relationship between two quantities where a change in one causes a corresponding change in the other. Student A claims F_max is directly proportional to the rod's radius, while Student B claims it is proportional to the cross-sectional area.
πŸ’‘Experimental Procedure
The experimental procedure outlines the steps to test how the maximum force depends on rod thickness. This involves measuring rod radius, attaching rods to a spring scale, and recording the force until the rod breaks, providing a systematic approach to data collection.
πŸ’‘Spring Scale
A spring scale is a device used to measure force by the amount a spring stretches. In the experiment, it is used to apply force to the rods and measure the force needed to break them, ensuring accurate force measurements.
πŸ’‘Linear Relationship
A linear relationship indicates a direct, straight-line correlation between two variables. Student A's model suggests a linear relationship between F_max and rod radius, implying that doubling the radius would double the maximum force.
πŸ’‘Quadratic Relationship
A quadratic relationship describes a parabolic correlation, where changes in one variable result in squared changes in another. Student B's model suggests a quadratic relationship between F_max and the cross-sectional area, meaning doubling the radius quadruples the maximum force.
πŸ’‘Radius (r)
Radius is the distance from the center of the rod's circular cross-section to its edge. It is crucial for calculating both the cross-sectional area and understanding the proportional relationships proposed by the students' models.
πŸ’‘Data Plotting
Data plotting involves graphically representing experimental results to identify trends or relationships. The video discusses plotting F_max against rod radius to compare linear and quadratic models, illustrating the importance of visual data representation in analysis.
Highlights

A group of students investigates how the thickness of a plastic rod affects the maximum force it can withstand before breaking.

Student A proposes that the maximum force (Fmax) is directly proportional to the radius of the rod.

Student B suggests that Fmax is directly proportional to the cross-sectional area of the rod.

The experiment involves measuring the radius of the rods and the force applied until they break using a spring scale.

The radius of the rod is measured with a meter stick or ruler, denoted as 'r'.

Fmax, the force applied before breaking, is measured with a spring scale, denoted as 'F'.

Procedure includes anchoring one end of the rod and attaching the other end to a spring scale, then pulling until the rod breaks.

Video recording of the force measurement may be used to accurately capture the force at the moment of breaking.

The experiment is repeated with rods of different radii to collect data on Fmax.

Student A's model predicts a linear relationship between Fmax and the radius of the rod.

Student B's model predicts a quadratic relationship between Fmax and the radius, due to the dependency on the cross-sectional area.

The data collected from the experiment will help determine which student's model is more accurate.

Data points are plotted with radius (r) on the x-axis and force (F) on the y-axis, showing the relationship between them.

The plotted data suggests a quadratic relationship, supporting Student B's model.

The conclusion is that the relationship between Fmax and the radius more closely matches a quadratic model, indicating dependence on the cross-sectional area.

Transcripts
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