# 2023 AP Physics 1 Free Response #1

TLDRThis video script tackles the 2023 AP Physics 1 free response questions, offering solutions with a promise of corrections in the comments. It delves into a cart-spring system's harmonic motion, explaining energy conservation with kinetic and potential energy graphs. The script also addresses the effect of adding a block to the system, calculating frequency changes and illustrating how the total energy remains constant, with kinetic and potential energy distribution shifting accordingly.

###### Takeaways

- π The transcript discusses the 2023 AP Physics 1 free response questions, with the speaker providing their best guess solutions since official solutions are not released yet.
- π The speaker mentions that any mistakes in their solutions will be corrected in a pinned comment in the video.
- π The script describes a physics problem involving a cart and a spring on a horizontal surface, where the system oscillates between two positions with negligible frictional forces.
- π The kinetic and potential energy of the system are graphed, with the x-intercept and y-intercept having the same values, which is explained by the conservation of energy.
- π The conservation of energy principle is emphasized, where the total energy remains constant at all times, with the energy being entirely kinetic or potential at the intercepts.
- π The x-intercept represents when all the energy is kinetic, and the y-intercept represents when all the energy is potential, both totaling four joules in the example given.
- π’ The speaker calculates the frequency of oscillation before and after a block is dropped onto the cart, using the formula for the period of a simple harmonic oscillator.
- β° The frequency of oscillation after the block is added is found to be half of the original frequency, indicating a longer period due to the increased mass.
- π The graph of kinetic versus potential energy remains identical after the block is added, explained by the fact that the total energy of the system does not change at the moment the block is dropped.
- π The script includes a sketch of the kinetic energy for the system consisting only of the cart and the spring after the block is added, showing how the energy is divided between the cart and the block.
- π€ The speaker provides a detailed explanation of the energy distribution between the cart and the block, highlighting that the block will have three times the kinetic energy of the cart due to its greater mass.

###### Q & A

### What type of motion is described in the 2023 AP Physics 1 released free response question involving a cart and a spring?

-The motion described is harmonic motion, where the system consisting of the cart and the spring oscillates between positions.

### Why are the x-intercept and y-intercept values the same on the graph of kinetic energy versus potential energy for the cart-spring system?

-The x-intercept and y-intercept values are the same because energy is conserved in the system. At the x-intercept, all the energy is kinetic, and at the y-intercept, all the energy is potential, both amounting to four joules.

### What is the significance of the block being dropped onto the cart in the scenario described?

-The block being dropped onto the cart increases the mass of the system, affecting the frequency of oscillation. The block sticks to the cart, and they continue to oscillate together.

### How does the frequency of oscillation change after the block is dropped onto the cart?

-The frequency of oscillation decreases after the block is dropped onto the cart because the period of oscillation increases due to the added mass.

### What is the relationship between the frequency of oscillation before and after the block is dropped onto the cart?

-The frequency after the block is dropped (F2) is half the frequency before the block was dropped (F1), as the period is longer with the additional mass.

### Why are the graphs of kinetic energy versus potential energy identical for the cart-spring system before and after the block is dropped?

-The graphs are identical because the total energy of the system remains the same, and the collision of the block with the cart does not change the potential energy at the moment of impact.

### What does the kinetic energy of the cart-spring system represent at the maximum point after the block is dropped?

-At the maximum point, the kinetic energy is split between the cart and the block, with the block having three times the energy of the cart due to its greater mass.

### How is the kinetic energy distributed between the cart and the block after the block is dropped onto the cart?

-The kinetic energy is distributed such that one joule corresponds to the kinetic energy of the cart, and the remaining three joules correspond to the kinetic energy of the block.

### What is the role of potential energy in the conservation of energy principle as described in the script?

-Potential energy plays a crucial role in the conservation of energy principle as it converts to kinetic energy and vice versa without any loss in the total energy of the system.

### Why is there no loss in energy in the cart-spring system as described in the script?

-There is no loss in energy because no external work is being done on the system, and the energy transitions between kinetic and potential forms without dissipation.

###### Outlines

##### π Analyzing the 2023 AP Physics 1 Free Response Questions

This paragraph discusses the 2023 AP Physics 1 exam's free response questions, noting the absence of official solutions until after scores are released. The speaker provides their own solutions, promising corrections in the comments if needed. The scenario involves a cart on a horizontal surface attached to a spring, oscillating due to the spring's force. The kinetic and potential energy graph is explained, with the x-intercept and y-intercept values being identical due to energy conservation. The speaker clarifies the meaning of these intercepts in the context of the system's energy states.

##### π Kinetic and Potential Energy Graphs Post-Block Attachment

The second paragraph delves into the effects of attaching a block to the cart during its oscillation. The kinetic and potential energy graph remains unchanged after the block is attached, which is explained by the conservation of the system's total energy at the moment of attachment. The block's addition does not alter the spring's potential energy, hence the total energy and the shape of the energy graph remain the same. The paragraph also addresses the change in frequency due to the increased mass, calculating the new frequency as half of the original, reflecting a longer period and a lower frequency due to the additional mass.

###### Mindmap

###### Keywords

##### π‘AP Physics 1

##### π‘Harmonic Motion

##### π‘Kinetic Energy

##### π‘Potential Energy

##### π‘Conservation of Energy

##### π‘X-intercept and Y-intercept

##### π‘Frequency of Oscillation

##### π‘Period

##### π‘Spring Constant (k)

##### π‘Momentum

##### π‘Collision

###### Highlights

The 2023 AP Physics 1 released free response questions are discussed without official solutions, as those are released after scores.

A cart on a horizontal surface is attracted to a spring, oscillating between positions in a harmonic motion when released.

The kinetic and potential energy graph shows the system's energy conservation with the same x and y intercept values, both at 4 Joules.

The x-intercept represents when all energy is kinetic (4 Joules) and the y-intercept when all energy is potential (4 Joules), due to energy conservation.

No energy loss occurs as no external work is being done on the system, maintaining energy conservation.

When the cart is momentarily at rest, a block is dropped under it and sticks, changing the system's dynamics.

The block-cart system continues to oscillate with increased mass, affecting the frequency of oscillation.

The frequency of oscillation before and after the block is dropped is calculated, showing a decrease in frequency with added mass.

The kinetic and potential energy graph remains identical after the block is dropped, indicating no change in total system energy.

The block's addition does not change the spring's potential energy, maintaining the system's total energy.

After the block is dropped, the cart-spring system's kinetic energy is redistributed, with the block having 3x the energy of the cart.

The kinetic energy graph for the cart-spring system after the block is dropped is sketched, showing the energy distribution between the cart and block.

The maximum kinetic energy is split into 1 Joule for the cart and 3 Joules for the block, reflecting the mass ratio.

The video provides a step-by-step explanation of the physics principles and calculations involved in the problem.

The importance of energy conservation and its implications on the system's behavior is emphasized throughout the explanation.

The video aims to clarify the concepts of kinetic and potential energy, frequency of oscillation, and the effects of mass on these properties.

The problem-solving approach demonstrates the application of physics principles to analyze and understand the system's behavior.

###### Transcripts

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