2019 AP Physics 1 Solutions Free Response #2

Allen Tsao The STEM Coach
9 May 201907:58
EducationalLearning
32 Likes 10 Comments

TLDRIn this educational video, Alan from Bothell STEM Coach explores the effects of relative masses on the acceleration of two connected blocks in a 2019 AP Physics problem. He discusses scenarios where one mass is significantly larger than the other and the case where both masses are comparable. Alan explains the concept using Newton's second law, free body diagrams, and net force equations to derive the acceleration formula in terms of masses and physical constants. The video also touches on the impact of a non-negligible pulley mass on tension and acceleration, providing a clear understanding of the dynamics involved.

Takeaways
  • 📚 The video is a tutorial by Alan from Bothell STEM, focusing on a 2019 AP Physics 1 free response question.
  • 🔍 The problem explores the effect of the relative masses of two blocks on their acceleration on a horizontal surface with negligible friction.
  • 📐 Block A has mass M and rests on a table, while Block B with mass P hangs from a light string attached to a pulley.
  • 🚫 The pulley has negligible mass and friction, and the blocks are released from rest.
  • ⚖️ If Block A's mass is significantly greater than Block B's, the acceleration of the blocks will be small due to the large mass.
  • 🔻 Conversely, if Block A's mass is much less than Block B's, the acceleration will be close to g, the acceleration due to gravity, as the small mass of A has minimal impact.
  • 🔄 When neither mass is significantly greater than the other, the acceleration will be determined by the combined effect of both masses on the system.
  • 📈 The video includes a free body diagram to illustrate the forces acting on each block and derives an equation for the blocks' acceleration in terms of their masses and physical constants.
  • 📉 In the scenario where mass A is much less than mass B, the acceleration is approximately equal to g, simplifying the equation to MB/g.
  • 🔧 The video also discusses the effect of a non-negligible mass pulley on the system, suggesting that it would reduce the tension in the string and the acceleration of the blocks.
  • 💬 Alan encourages viewers to share their experiences with the question and ask questions in the comments section.
Q & A

  • What is the main topic of the video?

    -The main topic of the video is the 2019 AP Physics 1 second free response question, which explores how the relative masses of two blocks affect their acceleration.

  • What assumptions are made about the friction and the pulley in the problem?

    -The assumptions are that there is negligible friction between block A and the tabletop, and the pulley has negligible mass and spins with negligible friction about its axis.

  • How does the mass of block A compare to the mass of block B in the first scenario?

    -In the first scenario, the mass of block A is much greater than the mass of block B.

  • What is the expected magnitude of acceleration when block A is much greater than block B?

    -The magnitude of acceleration is expected to be small because a small force is acting on a large mass, resulting in a small acceleration.

  • How does the acceleration of the blocks change when block A is much less than block B?

    -The acceleration of the blocks is close to g (acceleration due to gravity) because the small mass of block A does not significantly affect the system.

  • What should be done to the forces on block A and block B in the free body diagram?

    -For block A, tension acts to the right. For block B, tension acts upward and gravity acts downward, with the gravitational force being larger than the tension.

  • How is the net force equation for block A expressed?

    -The net force equation for block A is expressed as Ft = Ma * a, where Ft is the tension and Ma is the mass of block A.

  • How is the net force equation for block B expressed?

    -The net force equation for block B is expressed as Ft = Mb * g - Ft, where Ft is the tension, Mb is the mass of block B, and g is the acceleration due to gravity.

  • How is the acceleration of the blocks derived in terms of Ma and Mb?

    -The acceleration a is derived as a = Mb * g / (Ma + Mb) by combining the net force equations for blocks A and B.

  • How does the tension in the string compare when the pulley is not negligible?

    -The tension in the string (T2) when the pulley has mass is less than the tension (T1) when the pulley is negligible, because energy is spent on the rotational inertia of the pulley, resulting in a slower velocity and lower net acceleration.

Outlines
00:00
🔬 Physics Problem Analysis: Block Acceleration and Mass Ratio

In this segment, Alan from Bothell STEM introduces a 2019 AP Physics free response question. The problem examines how the relative masses of two blocks influence their acceleration. Block A with mass M lies on a frictionless table, while Block B with mass P hangs from a light string over a pulley. The system is released from rest, and the video explores different scenarios based on the mass ratio of A to B. Alan explains that if mass A is significantly larger, the acceleration will be small due to the small net force acting on the large mass. Conversely, if mass A is much smaller, the acceleration will be close to g, the acceleration due to gravity. When neither mass is significantly larger, the video suggests drawing force diagrams and deriving an equation for acceleration in terms of masses M and P, and physical constants.

05:01
📚 Deriving Acceleration Equation and Comparing Tensions

This paragraph continues the physics problem discussion, focusing on deriving an equation for the acceleration of the blocks after release, using the masses M and P. Alan simplifies the problem by ignoring the normal force and gravitational force since they cancel each other out. He sets up two net force equations, one for each block, and solves for the common acceleration 'a'. The resulting equation is a = (Mg)/(M + P). In a scenario where mass A is much less than mass B, the acceleration is approximately equal to g. The video then explores the effect of a non-negligible mass pulley on the system, comparing the tensions in the string (T1 and T2) and concluding that T2 would be less than T1 due to additional energy expenditure on the pulley's rotation, resulting in a slower acceleration.

Mindmap
Keywords
💡Bothell STEM
Bothell STEM is likely a reference to a science, technology, engineering, and mathematics (STEM) program or organization in Bothell, Washington. It is the context within which the speaker, Alan, is presenting the physics problem, suggesting that the video is educational in nature and aimed at students or educators interested in physics.
💡AP Physics
AP Physics refers to the Advanced Placement Physics courses and exams offered by the College Board. It is a high school course that prepares students for college-level physics and is a key concept in the video, as the problem being discussed is from the 2019 AP Physics exam, indicating the video's focus on academic preparation.
💡Free Response Question
A free response question is an open-ended question that requires a student to provide a detailed answer, often used in exams like the AP Physics to assess a student's understanding and ability to apply concepts. In the video, Alan is discussing a specific free response question from the 2019 AP Physics exam, which is central to the video's educational content.
💡Acceleration
Acceleration is the rate of change of velocity of an object with respect to time. It is a fundamental concept in physics and is the main focus of the problem discussed in the video. Alan uses the concept of acceleration to explore how the masses of two blocks affect their motion when connected by a string over a pulley.
💡Newton's Second Law
Newton's Second Law of Motion states that the force acting on an object is equal to the mass of that object times its acceleration (F = ma). This law is implicitly referenced in the video when discussing the relationship between force, mass, and acceleration in the context of the blocks' motion.
💡Friction
Friction is the force that resists the relative motion of two surfaces in contact. In the script, it is mentioned that there is negligible friction between block A and the tabletop, which simplifies the problem by eliminating one of the forces that could affect the blocks' acceleration.
💡Pulley System
A pulley system is a mechanical device that supports movement and a change in direction of a force applied. In the video, the pulley system is central to the problem, as it connects the two blocks and allows for the exploration of their acceleration when one block is lifted by the other.
💡Tension
Tension is the force transmitted through a string, rope, or cable when it is pulled tight by opposing forces. In the context of the video, tension is the force acting on both blocks through the string connected over the pulley, and it plays a critical role in determining the acceleration of the system.
💡Free Body Diagram
A free body diagram is a graphical representation used to visualize and analyze all the forces acting on an object. In the video, Alan discusses drawing free body diagrams for both blocks to understand the forces involved, such as tension and gravity, and how they contribute to the acceleration of the blocks.
💡Net Force
Net force is the vector sum of all the forces acting on an object. It is a key concept in the video as it is used to calculate the acceleration of the blocks. Alan explains that the net force on each block is the driving factor behind their motion, with the equation F_net = ma.
💡Mass Ratio
The mass ratio refers to the relationship between the masses of two or more objects. In the video, different scenarios are discussed based on the mass ratio of block A to block B, and how this ratio affects the acceleration of the system, which is a central theme of the problem being explored.
Highlights

Introduction to the 2019 AP Physics 1 Free Response Question exploring the effect of relative masses on the acceleration of two blocks.

Description of the experimental setup involving two blocks, a table, a pulley, and a string.

Assumption that the friction between block A and the tabletop is negligible.

Explanation of the forces acting on block A and block B, including tension and gravity.

Use of Newton's second law (F = MA) to estimate the magnitude of acceleration for different mass scenarios.

Estimation of acceleration when block A's mass is significantly greater than block B's mass.

Estimation of acceleration when block A's mass is much less than block B's mass, approaching the acceleration of gravity.

Discussion of the scenario where neither mass is significantly greater than the other.

Instruction to draw and label forces exerted on block A and block B for clarity.

Derivation of an equation for the acceleration of the blocks in terms of their masses and physical constants.

Consideration of a scenario where the mass of block A is much less than block B, leading to an approximation of acceleration equal to gravity.

Introduction of a second bullet with non-negligible mass to the pulley system.

Comparison of tensions in the string (T1 and T2) when the pulley mass is negligible and not negligible.

Explanation of how energy is spent on the rotation of the pulley with non-negligible mass, affecting acceleration.

Conclusion that T2 would be less than T1 due to energy expenditure on the pulley's rotation.

Invitation for viewers to share their experiences or questions regarding the problem in the comments.

Transcripts

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PhysicsAccelerationMassPulley SystemEducationalNewton's LawFrictionlessFree Body DiagramTension ForcesConcept Explanation