2019 AP Physics 1 Solutions Free Response #3
TLDRIn this educational video, Alan from Bothell STEM discusses a 2019 AP Physics free response question involving a spring launcher and a steel sphere. He explores the hypothesis that the spring constant may vary with compression distance. Alan suggests using the conservation of energy principle to test this, calculating the spring constant from measurable quantities like mass, velocity, and displacement. He outlines an experimental procedure using typical school physics lab equipment and explains how to analyze data to confirm or refute the hypothesis. The video also touches on the relationship between launch speed and mass, predicting an inverse square root graph.
Takeaways
- 🚀 The video discusses a physics experiment involving a projectile launcher with a spring and a plate to test the spring constant's consistency across different compression distances.
- 🔍 The experiment aims to verify if the spring constant remains the same regardless of the compression distance by using the principle of conservation of energy.
- 📐 The potential energy stored in the spring is expected to convert into the kinetic energy of the launched steel sphere, which is a key concept in the experiment.
- 📈 The expression for the spring constant (K) can be determined using measurements such as mass (M), velocity (V), and displacement (X), which are common in school physics labs.
- 📊 To find K, the formula \( K = \frac{MV^2}{2X^2} \) can be used, assuming the sphere does not spin and only translational kinetic energy is considered.
- 🌡 The mass of the sphere can be measured using a scale, and its velocity can be determined using a high-speed camera to track its movement over time.
- 📏 Displacement (X) is measured using a meter stick or ruler, which represents the initial distance the spring is compressed from its relaxed state.
- 🔬 The experimental procedure involves launching the sphere from different positions (A, B, C) and calculating K for each to see if it remains consistent.
- 📝 Data analysis involves comparing the calculated values of K for different positions to confirm or refute the hypothesis about the spring constant's behavior.
- 📉 If K values differ significantly between positions, it suggests the spring constant changes with compression distance; if similar, it supports the hypothesis of a constant K.
- 📌 In an additional scenario, the launcher is used to launch spheres of the same diameter but different masses from the same position to explore the relationship between mass and launch speed.
- 📉 The graph of launch speed (V) as a function of sphere mass (M) is expected to show an inverse square root relationship, indicating that heavier spheres will have lower launch speeds.
Q & A
What is the setup described in the script for launching the sphere?
-The setup consists of a projectile launcher with a spring and an attached plate. The spring can be compressed and held in place by a pin at three positions (A, B, or C). A steel sphere is placed against the plate, and the sphere is launched upon releasing the pin.
What hypothesis is the student trying to test in the experiment?
-The student hypothesizes that the spring constant inside the launcher has the same value for different compression distances.
Which physics principle is suggested for designing the experiment to test the hypothesis?
-The principle of conservation of energy is suggested. The potential energy stored in the compressed spring is converted into the kinetic energy of the sphere upon release.
How can the spring constant (k) be determined in the experiment?
-The spring constant (k) can be determined using the formula k = (mv²) / (x²), where m is the mass of the sphere, v is the velocity of the sphere, and x is the displacement of the spring.
What equipment is required to measure the necessary quantities in the experiment?
-A scale is needed to measure the mass of the sphere (m), a high-speed camera to measure the velocity (v), and a meter stick or ruler to measure the displacement of the spring (x).
What steps should be taken to test the hypothesis about the spring constant?
-The experiment involves measuring the mass, velocity, and displacement for different compression distances (positions A, B, C). The spring constant (k) is calculated for each position, and the values are compared to check for consistency.
How can the experimental data be analyzed to confirm or disconfirm the hypothesis?
-The values of the spring constant (k) calculated from the different positions (A, B, C) should be compared. If the values are consistent, the hypothesis is confirmed; if they differ significantly, the hypothesis is disconfirmed.
What is the expected relationship between the launch speed and the mass of the sphere, assuming the same compression distance?
-The launch speed (v) is expected to decrease as the mass (m) of the sphere increases. The relationship is inversely proportional to the square root of the mass, as given by the equation v = √(2E/m).
How would the graph of launch speed versus mass look, based on the relationship between them?
-The graph would show an inverse square root relationship, where the launch speed decreases as the mass increases. The curve starts high when the mass is low and gradually decreases as the mass increases.
What is the significance of using position sensors or velocity sensors in the experiment?
-Position sensors or velocity sensors can provide accurate measurements of the sphere's velocity, which is crucial for calculating the spring constant (k) and verifying the conservation of energy.
Outlines
🚀 Projectile Launcher Experiment
This paragraph introduces an experiment involving a projectile launcher with a spring and a plate. The launcher can be set to different compression distances by using pins at positions A, B, or C. The experiment's goal is to test the hypothesis that the spring constant remains the same regardless of the compression distance. The principle of conservation of energy is suggested for designing the experiment, where the spring's potential energy is converted into the kinetic energy of a steel sphere. The procedure involves measuring the mass of the sphere, its velocity using a high-speed camera, and the displacement of the spring. The spring constant is then calculated for different positions to compare and validate the hypothesis.
📉 Analysis of Spring Constant Variation
The second paragraph delves into the analysis of the experimental data to confirm or refute the hypothesis about the spring constant's consistency across different compression distances. It explains that the spring constant should be calculated for each compression point (A, B, C) and compared to determine if they are similar or different. The paragraph also discusses an additional experiment where spheres of the same diameter but varying masses are launched from the same position to observe the relationship between mass and launch speed. The expected graph of launch speed versus mass is described as an inverse square root function, suggesting that as mass increases, the launch speed decreases, and vice versa.
Mindmap
Keywords
💡Projectile Launcher
💡Spring Constant (K)
💡Conservation of Energy
💡Kinetic Energy
💡Potential Energy
💡Compression Distance (X)
💡High-Speed Camera
💡Velocity (V)
💡Mass (M)
💡Experimental Procedure
Highlights
Alan from Bothell STEM discusses a 2019 AP Physics free response question involving a projectile launcher.
The launcher consists of a spring with an attached plate that can be pinned at different positions.
A steel sphere is launched from the plate when the pin is released, simulating projectile motion.
Students hypothesize that the spring constant may vary with different compression distances.
The experiment aims to test this hypothesis using the principle of conservation of energy.
The potential energy of the spring is expected to convert into the kinetic energy of the sphere.
Expressions for spring constant are derived based on measurable quantities.
Equipment typically found in school physics labs will be used for the experiment.
The mass of the sphere will be measured using a scale.
Velocity will be measured using a high-speed camera to track the sphere's movement.
Displacement of the spring is measured with a meter stick or ruler.
The experimental procedure involves calculating the spring constant for different displacements.
The hypothesis will be confirmed or disconfirmed by comparing calculated spring constants.
Another experiment involves launching spheres of different masses from the same position.
The relationship between mass and launch speed is expected to follow an inverse square root function.
The graph of launch speed as a function of mass will illustrate this relationship.
The experiment's findings are intended to help students understand the principles of projectile motion and energy conservation.
Transcripts
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