2018 #5 Free Response Question - AP Physics 1 - Exam Solution

Flipping Physics

1 May 202009:42

EducationalLearning

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TLDRIn this engaging physics problem-solving session, the focus is on a 2018 AP Physics 1 free response question involving a mass-spring system. The video script walks through the step-by-step analysis of the problem, starting with calculating the period ratio of two blocks (P and Q) after block Q sticks to P, and then discussing the conservation of momentum and mechanical energy to determine the new amplitude of oscillation for the combined system. The solution to Part A reveals that the period of the P-Q system is the square root of 3 times the period of block P alone. For Part B, it's explained that the amplitude of the P-Q system is less than the original amplitude of block P due to the decrease in total mechanical energy upon the addition of block Q, which results in a reduced maximum kinetic energy and thus a smaller amplitude of oscillation.

Takeaways

📚 The problem involves a mass-spring system with block P and an additional block Q added to it.
🔄 Part A asks for the ratio of the periods of the two-block system (PQ) to the original block P, which is found using the formula for the period of a mass-spring system: 2π√(m/k).
🎈 The period of block P is given by 2π√(M/K), and after block Q is added, the mass becomes (M+2m), leading to a period ratio of √3.
💥 Part B discusses the change in amplitude due to the addition of block Q and the collision between blocks P and Q.
🚫 The amplitude of the PQ system is less than the amplitude of block P alone after the collision.
🔄 The collision is perfectly inelastic, meaning the blocks stick together and conserve momentum.
🌀 The conservation of mechanical energy is considered for the system after the collision, with no external work done.
📈 The decrease in total mechanical energy after adding block Q results in a decrease in maximum kinetic energy and thus a smaller amplitude.
📚 The problem is unusual as Part A is independent from Part B, unlike most AP exam questions.
📈 The paragraph argument in Part B may require more equations than usual, indicating a need for a deeper understanding of the physics involved.
🎓 The goal of the AP exam is to assess understanding of physics, not just recognition of patterns from previous exams, so careful reading is essential.

Q & A

What is the problem being discussed in the transcript?
-The problem involves solving a free response question from the 2018 AP Physics 1 exam, which is about a mass-spring system with two blocks, P and Q, and their oscillation periods and amplitudes.
What is the mass of block P?
-The mass of block P is denoted as M.
What is the mass of block Q?
-The mass of block Q is 2m.
How does block Q interact with block P?
-Block Q is dropped from rest and lands on block P at the equilibrium position, sticking to it immediately, forming a two-block system.
What is the formula for the period of a mass-spring system?
-The period of a mass-spring system is given by 2π times the square root of the ratio of the mass to the spring constant (T = 2π√(M/K)).
What is the ratio of the period of the two-block system (PQ) to the period of block P alone?
-The ratio of the period of the two-block system (T_PQ) to the period of block P alone (T_P) is the square root of 3 (T_PQ/T_P = √3).
How does the amplitude of the two-block system (PQ) compare to the amplitude of block P alone?
-The amplitude of the two-block system (a_PQ) is less than the amplitude of block P alone (a_P) because the addition of block Q decreases the total mechanical energy of the system, leading to a reduced amplitude.
What principle is conserved during the collision of block Q with block P?
-The principle of conservation of linear momentum is conserved during the collision of block Q with block P.
What principle applies when the blocks slide from the equilibrium position to the amplitude?
-The principle of conservation of mechanical energy applies when the blocks slide from the equilibrium position to the amplitude, as there are no external forces acting on the system.
How does the final velocity of the two-block system compare to the initial velocity of block P?
-The final velocity of the two-block system (V_PQ) at the equilibrium position is one-third of the initial velocity of block P (V_P) before the collision.
What happens to the mechanical energy of the system when block Q is added?
-When block Q is added, the mechanical energy of the system decreases to one-third of its previous value because the kinetic energy at the maximum displacement is reduced.
What is the significance of the independent parts in the AP Physics exam problem?
-The independent parts in the AP Physics exam problem, such as Part A and Part B in this case, require students to understand and solve each part separately, demonstrating their comprehensive grasp of the physics concepts involved.

Outlines

00:00

📚 Solving AP Physics 1 Free Response Question

The video begins with an introduction to solving a free response question from the 2018 AP Physics 1 exam. The problem involves a block (P) on a frictionless surface attached to a spring with constant (K) oscillating with period (T_sub_P) and amplitude (a_sub_P). A second block (Q) with mass 2m is dropped from rest and sticks to block P, resulting in a two-block system with a new period (T_sub_P_Q) and amplitude (a_sub_P_Q). The task is to determine the ratio of the periods of the two-block system to that of block P alone. Billy explains that the period of a mass-spring system is given by 2π times the square root of the mass over the spring constant. By applying this formula to both the single block P and the combined blocks P and Q, it is concluded that the ratio of the periods is the square root of 3.

05:01

🤔 Analysis of Block Collision and Amplitude

In the second part of the video, the focus shifts to Part B of the problem, which examines the amplitude of oscillation for the two-block system compared to the original block P. Bobby explains that the collision between block Q and P is perfectly inelastic, conserving linear momentum. The combined mass of the system decreases the velocity upon collision. The conservation of mechanical energy is then discussed, as the system transitions from the equilibrium position to the amplitude. It is concluded that the amplitude of the two-block system (P_Q) is less than the amplitude of block P alone, as the addition of block Q reduces the system's total mechanical energy, leading to a decrease in both kinetic and potential energy, and consequently, the amplitude of oscillation.

Mindmap

Keywords

💡AP Physics 1 exam

The AP Physics 1 exam is a standardized test administered by the College Board that assesses high school students' knowledge and understanding of introductory physics concepts. In the video, the exam serves as the context for solving a free response question, which is a part of the educational content being discussed and solved.

💡mass

In physics, mass is a measure of the amount of matter in an object, typically measured in kilograms (kg). It is a fundamental property that affects an object's inertia and gravitational interactions. In the context of the video, the mass of block P and block Q is crucial in determining their motion and the period of oscillation when attached to a spring.

💡spring constant

The spring constant, denoted by K, is a measure of the stiffness of a spring. It is defined as the force needed to extend or compress the spring by one unit of length. In the video, the spring constant is a key parameter in the equations used to calculate the period of oscillation for the mass-spring system.

💡oscillation

Oscillation refers to the repetitive back-and-forth motion of an object around an equilibrium position. In the context of the video, block P oscillates on a horizontal frictionless surface attached to a spring, and the problem involves calculating the period and amplitude of this oscillation.

💡period

The period of an oscillation is the time it takes for one complete cycle of the motion to occur. In physics problems involving springs and masses, the period is related to the mass and spring constant through a specific formula. In the video, the period is a critical concept used to compare the oscillation of a single block to the oscillation of two blocks combined.

💡amplitude

Amplitude in the context of oscillations is the maximum displacement of the oscillating object from its equilibrium position. It is a measure of the energy in the system. In the video, the amplitude is a key factor in analyzing the energy transfer during the collision of block Q with block P.

💡collision

A collision is an event in which two or more objects exert forces on each other for a very short time. In physics, collisions can be elastic (where kinetic energy is conserved) or inelastic (where some kinetic energy is converted to other forms). The video discusses a perfectly inelastic collision between block P and block Q, where they stick together after the collision.

💡momentum

Momentum is a vector quantity that represents the product of an object's mass and its velocity. The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In the video, momentum conservation is crucial in analyzing the collision between block P and block Q.

💡mechanical energy

Mechanical energy is the sum of potential and kinetic energies in a system. In a closed system with no external forces, the total mechanical energy remains constant, a principle known as the conservation of mechanical energy. The video discusses how mechanical energy is conserved when block Q lands on block P and they move together on the frictionless surface.

💡elastic potential energy

Elastic potential energy is the energy stored in a material when it is stretched, compressed, or deformed elastically. In the context of a spring, this energy is given by the formula (1/2) * spring constant * displacement^2. The video explains that when block Q is added to block P, the system's kinetic energy is converted into elastic potential energy, which affects the amplitude of the combined system's oscillation.

💡equilibrium position

The equilibrium position is the position where the net external force on an object is zero, and the object is either at rest or moving at a constant velocity. In the context of the video, the equilibrium position is the central point around which block P and the combined P and Q system oscillate.

Highlights

The problem is from the 2018 AP Physics 1 exam, focusing on a mass-spring system and the effects of adding a second block.

Block P has mass M and is oscillating on a frictionless surface with a spring of constant K.

Block Q, with mass 2m, is dropped and sticks to block P at the equilibrium position, forming a two-block system.

The period of the two-block system (PQ) is derived using the mass-spring formula, resulting in a period of 2π times the square root of (3M/K).

The ratio of the periods is the square root of 3, indicating that the period of the two-block system is longer than that of block P alone.

Part B of the problem examines the change in amplitude of oscillation when block Q is added to block P.

The collision between block Q and P is perfectly inelastic, and momentum is conserved during this process.

The final velocity of the PQ system is one-third of the initial velocity of block P.

The addition of block Q results in a decrease in the total mechanical energy of the system.

The amplitude of the PQ system is less than the amplitude of block P alone due to the conversion of kinetic energy to elastic potential energy.

The spring constant remains unchanged, and the decrease in amplitude is a direct result of the reduced mechanical energy.

The problem requires a clear, coherent paragraph-length response that includes both explanation and equations.

The grading notes emphasize that the problem's parts are independent, and the physics of Part A does not relate to Part B.

The AP exam aims to assess understanding of physics, not just recognition of patterns from previous exams.

Students should be prepared for a variety of question types and not assume similarity with past exams.

The problem-solving process involves a combination of conservation of momentum and mechanical energy principles.

The final equilibrium position will be at the amplitude, where all kinetic energy is converted to elastic potential energy.

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Takeaways

Q & A

What is the problem being discussed in the transcript?

What is the mass of block P?

What is the mass of block Q?

How does block Q interact with block P?

What is the formula for the period of a mass-spring system?

What is the ratio of the period of the two-block system (PQ) to the period of block P alone?

How does the amplitude of the two-block system (PQ) compare to the amplitude of block P alone?

What principle is conserved during the collision of block Q with block P?

What principle applies when the blocks slide from the equilibrium position to the amplitude?

How does the final velocity of the two-block system compare to the initial velocity of block P?

What happens to the mechanical energy of the system when block Q is added?

What is the significance of the independent parts in the AP Physics exam problem?