2019 #3 Free Response Question - AP Physics 1 - Exam Solution
TLDRIn this engaging physics problem-solving discussion, the focus is on designing an experiment to test the hypothesis that the spring constant in a projectile launcher remains the same across different compression distances. The group explores various experimental setups, ultimately deciding on a horizontal launch to measure the sphere's launch speed using a motion sensor. They detail the procedure, emphasizing the importance of reducing experimental uncertainty by conducting multiple trials. The analysis of the data involves graphing the results, with the spring constant represented by the slope of the best-fit line. The session concludes with a consideration of how the launch speed varies with the mass of the spheres, confirming the inverse relationship as mass increases and velocity decreases.
Takeaways
- 📝 The problem discussed is a free response question from the 2019 AP Physics 1 exam, focusing on testing a hypothesis about the spring constant in a projectile launcher.
- 🔍 Part A requires identifying a basic physics principle or law to design an experiment, which is the conservation of mechanical energy.
- 🎯 To determine the spring constant, an expression is derived using the conservation of mechanical energy principle, relating it to the mass of the sphere, its final velocity, and the initial displacement.
- 🔧 Part B involves designing an experimental procedure to test the hypothesis using the launcher, which includes measuring quantities and using specific equipment found in a school physics lab.
- 🌟 The experimental design chosen involves launching the sphere horizontally and measuring its launch speed, which simplifies calculations by eliminating changes in gravitational potential energy.
- 📈 Conducting the experiment multiple times at each pin location and using a motion sensor to measure the sphere's speed helps reduce experimental uncertainty.
- 📊 Part C describes how to analyze the experimental data by plotting a graph with the spring constant as the slope to confirm or disprove the hypothesis.
- 🔄 Part D considers another scenario where spheres of different masses are launched consecutively from the same position, and a graph of launch speed vs. sphere mass is sketched to understand the inverse relationship.
- 🎓 The problem-solving process emphasizes the importance of reading the entire question before starting to answer, to ensure all parts are addressed thoroughly.
- 🤔 The discussion highlights the need for careful experimental design and the use of graphs to visually confirm or refute a physical hypothesis.
- 👩🏫 The script serves as a learning tool, demonstrating how to approach and solve a physics problem step by step, including the critical thinking involved in scientific experimentation.
Q & A
What is the main topic of the discussion in the transcript?
-The main topic is the analysis and solution of a free response question from the 2019 AP Physics 1 exam, which involves a projectile launcher and the concept of spring constant.
What is the hypothesis proposed by the student in the problem?
-The student hypothesizes that the spring constant of the spring inside the launcher remains the same for different compression distances.
What is the basic physics principle used to design the experiment in Part A I?
-The basic physics principle used is the conservation of mechanical energy.
How is the spring constant expressed in terms of measurable quantities according to the discussion?
-The spring constant is expressed as the mass of the sphere times the final velocity of the sphere squared, all divided by the square of the initial displacement of the sphere from the equilibrium position.
What experimental procedure is suggested to test the hypothesis?
-The suggested procedure involves launching the sphere horizontally, measuring the mass of the sphere, the displacement of the spring, and the speed of the sphere as it leaves the launcher. The experiment should be conducted multiple times at each pin location to reduce experimental uncertainty.
How can the experimental data be analyzed to confirm or disconfirm the hypothesis?
-The data can be analyzed by creating a graph with the spring constant as the slope. The y-axis should have the mass of the sphere times the square of the final velocity, and the x-axis should have the square of the initial displacement from the equilibrium position. If the slope and y-intercept are within experimental error, the hypothesis is confirmed.
What is the relationship between the mass of the sphere and its launch speed according to the rearranged equation?
-The relationship is inverse; as the mass of the sphere increases, the launch speed decreases.
What type of graph should be sketched for Part C of the problem?
-A graph of launch speed as a function of sphere mass, with the launch speed on the y-axis and the mass of the sphere on the x-axis, showing an inverse relationship between mass and launch speed.
How does the shape of the curve in the graph for Part C look?
-The curve should be concave up and decreasing, resembling a graph of y equals 1 over the square root of x, which is closer to both axes for smaller masses and further away for larger masses.
What is the significance of the y-intercept in the graph for Part C?
-The y-intercept should be near zero. If it is within experimental error, it confirms the student's hypothesis about the spring constant.
What is the launcher's orientation in the suggested experimental design?
-The launcher is oriented horizontally for the suggested experimental design.
Outlines
🚀 Physics Experiment Design: Projectile Launcher Hypothesis
This paragraph introduces a physics problem from the 2019 AP Physics 1 exam, focusing on a projectile launcher with a spring mechanism. The scenario involves a steel sphere launched from the launcher, with the hypothesis that the spring constant remains the same across different compression distances. The paragraph discusses the experimental design process, emphasizing the importance of reading the entire problem before starting. It suggests potential experiments, such as launching the sphere horizontally and measuring its launch speed, and highlights the conservation of mechanical energy as the underlying physics principle. The paragraph concludes with the expression for the spring constant derived from the conservation of mechanical energy equation.
📏 Measuring Procedure for Spring Constant Experiment
This paragraph outlines the experimental procedure to test the spring constant hypothesis using the projectile launcher. It details the steps to be taken, including measuring the mass of the sphere, setting up the launcher horizontally, and recording the initial position of the spring. The paragraph emphasizes the need to measure the displacement of the spring from its equilibrium position and to use a motion sensor to determine the sphere's launch speed. It also mentions the importance of conducting the experiment multiple times at each pin location to reduce experimental uncertainty. The paragraph concludes with a reminder to use the launcher as specified in the question and to answer the entire question carefully.
📈 Data Analysis for Spring Constant Confirmation
This paragraph discusses the analysis of experimental data to confirm or disprove the hypothesis regarding the spring constant's consistency across different compression distances. It suggests creating a graph with the spring constant as the slope, using the derived equation. The y-axis would represent the mass of the sphere times the square of the final velocity, while the x-axis would represent the square of the initial displacement from the equilibrium position. The graph should ideally show a best-fit line with a slope equal to the spring constant and a y-intercept near zero, which would confirm the hypothesis within the bounds of experimental error. The paragraph concludes with a summary of the expected graph shape and the interpretation of the data in relation to the hypothesis.
🌐 Graphing Launch Speed vs. Sphere Mass
The final paragraph addresses another aspect of the experiment where different spheres with varying masses are launched consecutively from the same position. It focuses on sketching a graph of launch speed as a function of sphere mass. The equation is rearranged to solve for the final speed of the sphere, revealing an inverse relationship between mass and launch speed. The graph is expected to show a curve that is concave up and decreasing, with the shape of the curve being the key focus rather than the precise mathematical accuracy. The paragraph concludes with a whimsical note about whistling while drawing graphs, highlighting the collaborative and engaging nature of the learning process.
Mindmap
Keywords
💡Projectile Launcher
💡Spring Constant
💡Conservation of Mechanical Energy
💡Experimental Design
💡Horizontal Launch
💡Motion Sensor
💡Data Analysis
💡Gravitational Potential Energy
💡Elastic Potential Energy
💡Hooke's Law
💡Mechanical Energy
Highlights
The problem at hand involves solving a free response question from the 2019 AP Physics 1 exam, focusing on a projectile launcher mechanism.
The launcher operates using a spring attached to a plate, which can be compressed and held at different positions.
A steel sphere is launched from the launcher when a pin holding the plate is released.
The student's hypothesis is that the spring constant remains the same for different compression distances.
The experiment aims to test the hypothesis by launching the sphere with the launcher.
The basic physics principle used in designing the experiment is the conservation of mechanical energy.
An expression for the spring constant is derived using the conservation of mechanical energy principle.
The experimental design involves launching the sphere horizontally and measuring its launch speed.
The mass of the sphere and the initial displacement of the spring from the equilibrium position are key measurable quantities.
The speed of the sphere as it leaves the launcher is crucial for determining the spring constant.
Conducting the experiment multiple times at each pin location helps reduce experimental uncertainty.
Data analysis involves creating a graph with the spring constant as the slope to confirm or disprove the hypothesis.
The graph should show a best-fit line with a slope equal to the spring constant and a y-intercept near zero.
Another aspect of the problem involves launching spheres of different masses from the same position and analyzing the launch speed as a function of mass.
The relationship between launch speed and mass is inversely proportional, with lighter spheres having higher launch speeds.
The graph of launch speed vs. mass should exhibit an inverse relationship, not necessarily a straight line.
The problem-solving process emphasizes the importance of careful reading, understanding the entire question, and the significance of experimental design.
The problem also highlights the practical application of theoretical physics principles in real-world scenarios, such as designing and conducting experiments.
The discussion underscores the value of collaboration and peer feedback in the learning process.
Transcripts
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