2015 AP Physics 1 Free Response #5

Allen Tsao The STEM Coach
28 Sept 201807:05
EducationalLearning
32 Likes 10 Comments

TLDRIn this video, Alan from Bothell STEM Coach reviews the AP Physics 1 2015 free response questions. He discusses the peculiarities of the test, focusing on a problem involving strings with different fundamental frequencies. Alan explains the physics concepts involved, such as velocity, wavelength, and linear mass density, and walks through the mathematical reasoning. He also addresses how the frequency changes when the string vibrates in its second harmonic. The video concludes with an invitation to join Alan on Twitch or Discord for free homework help and more discussions on math and physics.

Takeaways
  • πŸ“š The video is a review of the AP Physics 1 2015 free response questions by Alan, a Bothell stem coach.
  • πŸ” The test was unusual as it was the first year for the new exam format, and the presenter believes the questions are still being refined.
  • πŸŽ“ The problem discussed involves a string attached to an oscillator and a block, passing over a massless pulley with negligible friction.
  • πŸ”„ All strings are set side-by-side with the same distance between the oscillator and pulley, and the same mass for each block, but different fundamental frequencies.
  • πŸŒ€ The key to solving the problem is understanding that the different fundamental frequencies imply different velocities (V) despite the same wavelength (Ξ»).
  • πŸ“‰ The velocity equation provided is crucial as it relates velocity to the wavelength and frequency (V = Ξ» * F).
  • πŸ”§ The mass (M) and the force due to tension (FT) are the same for all strings, leading to the conclusion that the mass of the rope must vary to cause different frequencies.
  • πŸ“‰ The frequency of a string is inversely proportional to its linear mass density, which is a nonlinear relationship.
  • πŸ“š The video explains that the linear mass density is calculated as the square root of (FT/M/L), which is different for each string due to varying velocities.
  • 🎢 The video also discusses the second harmonic of string D, indicating a change in the vibration pattern of the string.
  • πŸ‘¨β€πŸ« Alan offers free homework help on platforms like Twitch or Discord for those interested in further learning or assistance with math and physics.
Q & A
  • What is the context of the video transcript?

    -The video transcript is from Alan at Bothell STEM Coach, discussing and wrapping up the AP Physics 1 2015 free response questions.

  • What is unique about the AP Physics 1 2015 exam according to Alan?

    -Alan mentions that the AP Physics 1 2015 exam was the first year they conducted this exam, and he believes they are improving and standardizing the questions.

  • What setup is described in the physics problem discussed in the video?

    -The setup described involves a string attached to an oscillator on one end and a block on the other, passing over a massless pulley system with negligible friction. Four such strings, labeled A, B, C, and D, are set side-by-side, with each oscillator vibrating the string at a fundamental frequency F, and all strings having the same length L and block mass M.

  • Why do the four strings have different fundamental frequencies?

    -The four strings have different fundamental frequencies because the velocity of the wave on each string is different. Given that the length and tension are the same for all strings, the differing velocities imply different linear mass densities for the strings.

  • How is the velocity of the wave on the string related to the fundamental frequency and wavelength?

    -The velocity (V) of the wave on the string is equal to the product of the wavelength (Ξ») and the frequency (F). Since the length of the string (L) and the wavelength are the same, differences in frequency imply differences in velocity.

  • What is the relationship between frequency and linear mass density?

    -The frequency of the wave is inversely proportional to the square root of the linear mass density of the string, meaning that as the mass per unit length increases, the frequency decreases.

  • Is the relationship between frequency and linear mass density linear?

    -No, the relationship is not linear. The frequency is proportional to the inverse square root of the linear mass density, which is a nonlinear relationship.

  • What change is made to the oscillator connected to string D?

    -The frequency of the oscillator connected to string D is changed so that it vibrates in its second harmonic.

  • Where are the points of greatest average vertical speed on a string vibrating in its second harmonic?

    -The points of greatest average vertical speed on a string vibrating in its second harmonic are at the positions corresponding to the antinodes, which are one-third and two-thirds of the way along the length of the string.

  • What conclusion can be drawn from the fact that the blocks have the same mass and the strings have different frequencies?

    -Since the blocks have the same mass, the tension in each string (FT) is the same. Given the same length (L) and different frequencies (F), the differing velocities (V) indicate that the linear mass densities (ΞΌ) of the strings must be different, resulting in different fundamental frequencies.

Outlines
00:00
πŸ” Overview of the AP Physics 1 2015 Exam and Fundamental Frequency Concept

Alan from Bothell STEM Coach introduces the final review of the AP Physics 1 2015 free response questions. He comments on the uniqueness of the test as it was the first year the exam was conducted. The main discussion revolves around the fundamental frequencies of strings attached to an oscillator, the same length (L), and mass (M). He explains that despite having the same length and mass, the fundamental frequencies vary due to differences in the linear mass density of the strings. This implies that the velocity of the waves in the strings varies, which is derived from the relationship between frequency, wavelength, and velocity.

05:01
πŸ“ Detailed Explanation of Wave Velocity and Linear Mass Density Relationship

Alan delves deeper into the physics concepts by breaking down the equations involved. He explains that the velocity of the wave is a function of the tension in the string (FT) and the linear mass density (ΞΌ). Since the blocks are stationary and not accelerating, the tension FT is equal to the weight of the blocks (Mg). Thus, the variations in wave velocity are attributed to the differences in the linear mass density of the strings. Alan concludes that different mass densities lead to different wave velocities, resulting in different fundamental frequencies.

🎼 Harmonic Motion and Maximum Vertical Speed Points

Alan illustrates the second harmonic of the vibrating string connected to oscillator D. He describes the points on the string that have the greatest average vertical speed during the oscillation. These points, known as antinodes, are where the string moves up and down the most. He identifies these positions in the wave diagram, emphasizing their significance in harmonic motion.

πŸ”— Conclusion and Availability for Further Help

Alan wraps up the discussion by summarizing the key points about the varying linear mass densities and their impact on wave velocity and fundamental frequencies. He shares his opinion on the difficulty and nature of the exam questions. Alan encourages viewers to leave comments, like, or subscribe to the channel. He also invites them to join his free homework help sessions on Twitch or Discord, offering assistance in math and physics.

Mindmap
Keywords
πŸ’‘AP Physics 1
AP Physics 1 is a college-level course and exam offered by the College Board that covers foundational concepts in physics, including mechanics, energy, and sound. In the video, the speaker is discussing the 2015 free response questions, indicating that the video's theme revolves around analyzing and understanding these exam questions to improve students' comprehension and performance.
πŸ’‘Oscillator
An oscillator is a system that experiences a restoring force and oscillates about an equilibrium position. In the context of the video, the oscillator is attached to one end of a string, which is a key part of the physics problem being discussed. The oscillator's function is to vibrate the string at a certain frequency, which is central to the problem's analysis.
πŸ’‘Fundamental Frequency
The fundamental frequency is the lowest frequency of vibration that a system can exhibit. In the script, it's mentioned that each string has a different fundamental frequency, which is a critical aspect of the problem. The differences in these frequencies are what the speaker is trying to explain and understand through the video.
πŸ’‘Wavelength
Wavelength is the physical distance between two consecutive points in a wave that are in the same phase of oscillation. The video script mentions that the wavelength is the same for all strings because they are of the same length, which is a key observation in determining why the fundamental frequencies differ.
πŸ’‘Velocity
Velocity is the rate at which an object changes its position. In the context of the video, the speaker uses the velocity equation to explain the relationship between frequency, wavelength, and the mass of the string. The velocity is different among the strings due to the different fundamental frequencies, which is a key point in the analysis.
πŸ’‘Linear Mass Density
Linear mass density is the mass per unit length of an object. The video explains that the different fundamental frequencies are due to the different linear mass densities of the strings, even though their lengths are the same. This concept is crucial to understanding why the strings vibrate at different frequencies.
πŸ’‘Freebody Diagram
A freebody diagram is a simplified representation of all the forces acting on an object. In the script, the speaker mentions using a freebody diagram to analyze the forces on the block attached to the string, which helps in understanding the relationship between the tension in the string and the gravitational force on the block.
πŸ’‘Harmonic
A harmonic is a frequency that is an integer multiple of the fundamental frequency. The video script refers to the second harmonic, which is twice the fundamental frequency. This is an important concept when discussing the different vibrational modes of the string.
πŸ’‘Average Vertical Speed
Average vertical speed is the mean rate at which an object moves vertically. In the context of the video, the speaker identifies points on the string with the greatest average vertical speed, which is relevant to understanding the motion of the string and its vibrational modes.
πŸ’‘Twitch and Discord
Twitch and Discord are platforms where the speaker offers free homework help. Mentioning these platforms in the video script is a way to engage with the audience and provide additional resources for learning and asking questions about math and physics.
πŸ’‘Homework Help
Homework help refers to assistance provided to students with their assignments. In the video, the speaker offers this service on Twitch and Discord, indicating a commitment to supporting students beyond the content of the video itself.
Highlights

Alan from Bothell STEM Coach discusses AP Physics 1 2015 free response questions.

The test is noted as being a bit strange, being the first year of its kind.

The exam questions are believed to be improving and becoming more standardized.

A string with one end attached to an oscillator and the other to a block is described.

The string passes over a massless pulley system with negligible friction.

Strings ABC and D are set side-by-side with the same oscillator to pulley distance L.

Each block has the same mass M, but the fundamental frequency of each string varies.

The difference in fundamental frequencies is attributed to different linear mass densities.

The velocity equation is introduced as a key factor in understanding the differences.

The wavelength lambda is the same for all strings due to the same length L.

Different fundamental frequencies imply different velocities among the strings.

The mass of the rope must be different to account for the varying velocities.

Frequency is a function of the inverse of the linear mass density, not a linear relationship.

The second harmonic of string D is discussed with an emphasis on average vertical speed.

The points of maximum average vertical speed are identified in the string's motion.

The importance of the same wavelength and different velocities for different linear mass densities is reiterated.

Alan offers free homework help on Twitch or Discord for those interested in math and physics.

The video concludes with an invitation for comments, likes, subscriptions, and participation in the community.

Transcripts
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