# 6 | FRQ | Practice Sessions | AP Physics C: Mechanics

TLDRIn this AP Daily Practice Session, physics teacher Dee Dee Messer from William Mason High School guides students through a free response question on linear mechanics. The session covers topics such as drawing free-body diagrams, using conservation of momentum, and deriving expressions for kinetic energy and maximum compression of a spring. Messer emphasizes careful work and accurate representations, explaining the importance of understanding and correctly applying physical principles. The video encourages practice to prepare for the AP exam, offering valuable insights and tips for scoring well.

###### Takeaways

- π The session is an AP Daily Practice for Mechanics, led by physics C teacher Dee Dee Messer.
- π The scenario involves a block of mass 2M at rest on a horizontal table attached to a nonlinear spring, and a block of mass 3M moving to the left with initial velocity v0.
- βοΈ The spring's force obeys the equation F = -Bx^3, where B is a positive constant and x is the displacement from equilibrium.
- π Free-body diagrams are crucial for visualizing the forces acting on each block before they collide, emphasizing accuracy and distinct labeling.
- π Part a of the exercise is worth two points, focusing on correct force representation and labeling for both blocks.
- π In part b, the conservation of momentum is used to derive the expression for the speed of the blocks immediately after the collision.
- π For part c, the kinetic energy of the two-block system is determined using the velocity found in part b.
- π Part d requires deriving an expression for the maximum spring compression distance D using conservation of energy principles.
- π The spring's non-ideal nature is considered in part d, leading to a complex but correct expression for maximum compression.
- π In part e, the direction and magnitude of the net force on the blocks at maximum spring compression are discussed, emphasizing the need for concise and correct justifications.
- π The final part of e addresses whether the blocks exhibit simple harmonic motion post-collision, concluding that they do not due to the nonlinear restoring force.
- π― The importance of practice is highlighted for better performance in the AP exam, encouraging continued engagement with the material.

###### Q & A

### What is the purpose of the AP Daily Practice session presented by Dee Dee Messer?

-The purpose of the session is to practice solving a free response question related to linear mechanics, providing guidance on how to approach the problem and offering insights into the scoring guidelines for the AP exam.

### What is the significance of drawing free-body diagrams accurately in the context of this session?

-Free-body diagrams are crucial for accurately depicting the forces acting on an object. In the session, it is emphasized that arrows must start on the dot and point away from it, as incorrect drawings may not be counted towards the score.

### What is the initial condition of the block of mass 2M in the given scenario?

-The block of mass 2M is at rest on a horizontal table and is attached to a relaxed spring, which is the equilibrium position.

### What is the force equation that the spring obeys in this scenario?

-The spring obeys a nonlinear force equation, which is F equals negative Bx cubed, where B is a positive constant and x is the displacement from equilibrium.

### What is the initial velocity of the block of mass 3M, and in which direction is it moving?

-The block of mass 3M has an initial velocity of v0 and is moving to the left.

### Why is friction considered negligible in this problem, and what is its implication?

-Friction is considered negligible because it is not mentioned as a factor in the initial conditions. This implies that there are no horizontal forces acting on the blocks, simplifying the analysis of forces.

### How does the conservation of momentum principle apply to part b of the problem?

-In part b, the conservation of momentum principle is applied to derive the expression for the speed of the blocks immediately after the collision, where the total initial momentum is equal to the total momentum after the collision.

### What is the expression for the kinetic energy of the two-block system after they have collided and are moving together?

-The expression for the kinetic energy of the two-block system is \( \frac{9}{10} Mv_0^2 \), which is derived by substituting the mass of the system and the velocity from part b into the kinetic energy formula.

### How is the maximum distance D that the spring is compressed related to the initial kinetic energy and the spring force?

-The maximum distance D is derived using the conservation of energy principle, where the initial kinetic energy is converted into potential energy at maximum compression. The spring force, being non-linear, is integrated over the distance D to find the relationship.

### What is the scoring guideline for part d of the problem, and what are the key points to earn full marks?

-Part d is worth four points, with one point for using a conservation of energy expression, one point for integrating the spring force equation correctly, one point for using the correct limits of integration or a constant of integration, and one point for using the kinetic energy expression consistent with part b.

### Why do the two blocks not exhibit simple harmonic motion after the collision, as explained in part e of the problem?

-The two blocks do not exhibit simple harmonic motion because the restoring force exerted by the spring is not linear and therefore not proportional to the displacement from equilibrium, which is a requirement for simple harmonic motion.

###### Outlines

##### π Mechanics Session Introduction and Scenario Setup

In this segment, the host, Dee Dee Messer, a physics C teacher, introduces an AP Daily Practice session focused on linear mechanics. She provides a PDF link for reference and suggests viewers can pause the video to answer questions independently. The scenario involves a block of mass 2M on a horizontal table attached to a relaxed, nonlinear spring with a force equation F = -Bx^3. Another block of mass 3M moves to the left with an initial velocity v0. Friction is negligible. The task is to draw and label forces acting on each block before they collide, emphasizing the importance of accurate free-body diagrams for understanding the scenario.

##### π Collision Analysis and Energy Conservation

This paragraph delves into the physics of the collision between the two blocks, emphasizing the conservation of linear momentum. The host derives the expression for the velocity of the combined blocks after the collision, which is 3/5 v0. The kinetic energy of the system is then calculated using the derived velocity. The paragraph also covers the process of deriving the maximum compression distance D of the spring using energy conservation principles. The host integrates the non-ideal spring force equation over the distance D to find the expression for D in terms of the given variables, highlighting the importance of correct variable substitution and integration limits.

##### π Post-Collision Dynamics and Simple Harmonic Motion

The final paragraph addresses the dynamics of the two blocks after the collision. It begins with a question about the net force direction on the 2M block at maximum spring compression, correctly identifying it as to the right. The host explains that the spring exerts a force to the right to decelerate the blocks, which were initially moving to the left. The magnitude of the net force on each block is then discussed, with the 3M block experiencing a greater force due to its larger mass and the same acceleration. Lastly, the paragraph refutes the possibility of the blocks exhibiting simple harmonic motion post-collision, justifying this with the non-linear nature of the spring's restoring force. The host wraps up by encouraging continued practice for better AP exam performance.

###### Mindmap

###### Keywords

##### π‘Free-body diagram

##### π‘Conservation of momentum

##### π‘Kinetic energy

##### π‘Nonlinear spring

##### π‘Maximum compression

##### π‘Simple harmonic motion

##### π‘Net force

##### π‘Gravitational force

##### π‘Normal force

##### π‘Conservation of energy

###### Highlights

Introduction to AP Daily Practice Session for Mechanics with Dee Dee Messer, focusing on a free response question related to linear mechanics.

Description of the scenario with a block of mass 2M at rest, a nonlinear spring, and a block of mass 3M with initial velocity.

Explanation of how to draw and label free-body diagrams for both blocks before collision, highlighting the importance of accurate vector representation.

Emphasis on using the conservation of momentum to derive the expression for the speed of blocks immediately after the collision.

Derivation of the expression for the kinetic energy of the two-block system after collision.

Use of conservation of energy to derive the expression for the maximum distance D that the spring is compressed.

Clarification of the need to use the correct spring force equation and integration limits when solving for potential energy.

Explanation of the direction of net force on block 2M at maximum compression of the spring, with justification based on system motion.

Discussion on the magnitude of net force on each block at maximum compression, emphasizing the relationship between force, mass, and acceleration.

Explanation of why the motion after the collision does not exhibit simple harmonic motion due to the nonlinear nature of the spring force.

Reminder to provide justifications for answers, especially in questions involving checks and explanations.

Advice to attempt all parts of a question, even if unsure, to maximize scoring opportunities.

Emphasis on concise and precise answers, especially in justifications, to avoid losing points due to over-explanation.

Encouragement to continue practicing and watching practice sessions for better results on the AP exam.

Final message wishing students good luck and encouraging continued practice.

###### Transcripts

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