Advanced Placement

24 Apr 202314:40

EducationalLearning

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TLDRIn this AP Physics Daily Practice video, instructor Dee Dee Messer guides students through a free response question on simple harmonic motion. The session covers deriving expressions for velocity and position, calculating the spring constant, drawing free body diagrams for a block on a rough surface, and sketching a velocity versus time graph for damped oscillation. The video emphasizes the importance of understanding the principles and practicing to achieve better results on the AP exam.

###### Takeaways

- 📚 This video is part of the AP Physics Daily Practice series, focusing on Mechanics and simple harmonic motion.
- 👩🏫 The presenter is Dee Dee Messer, an AP Physics teacher at William Mason High School in Ohio.
- 🔗 Viewers are encouraged to download a PDF of the question or pause the video to work through the problem alongside the presentation.
- 📊 The video includes a motion detector graph showing velocity versus time for a block attached to a spring.
- 📐 The positive direction for all quantities in the video is to the right, which is crucial for understanding the direction of motion.
- 📘 For part a, the task is to derive an expression for velocity with all constants substituted with numerical values.
- 📉 The velocity expression is derived from the position-time graph, considering the motion is simple harmonic and the phase constant is zero.
- 🔢 The maximum velocity (v_max) is approximately 16 m/s, and the angular frequency (omega) is calculated using the period found from the graph, which is 0.7 seconds.
- 💯 Scoring guidelines for part a emphasize the importance of the correct trigonometric expression, the use of 2π/period for omega, and the correct use of the graph to find the period and maximum velocity.
- 📐 For part b, the task is to derive an expression for position as a function of time, integrating the velocity expression from part a.
- 🔑 The spring constant (k) is calculated in part c using the formula relating the period and spring constant, with the mass and period values from the problem statement.
- 📝 In part d, free body diagrams are drawn for two different scenarios when the block is on a rough surface, showing the forces acting on the block at different positions and motions.
- 📈 Part e involves sketching a velocity versus time graph for the scenario with a rough surface, showing a damped oscillation with a decreasing amplitude but constant period.
- 🏆 The video concludes with a reminder of the importance of practice for success on the AP exam.

###### Q & A

### What is the topic of the video session presented by Dee Dee Messer?

-The topic of the video session is AP Physics Daily Practice, focusing on Mechanics, specifically a free response question on simple harmonic motion.

### What is the mass of the block used in Experiment 1 as described in the script?

-The mass of the block used in Experiment 1 is 0.3 kilograms.

### What is the purpose of the motion detector in the experiment?

-The motion detector is used to record the position of the block as it oscillates, which helps in creating a velocity versus time graph.

### What is the significance of the positive direction in the experiment?

-The positive direction is significant as it helps in determining which direction the positive and negative values will refer to in the experiment's measurements and graphs.

### How is the velocity of the block related to its position in simple harmonic motion according to the script?

-The velocity of the block is the derivative of its position with respect to time, and for simple harmonic motion, it is given by the expression -v_max * sine(omega * t), where v_max is the maximum velocity and omega is the angular frequency.

### What is the period of the block's oscillation as determined from the graph in the script?

-The period of the block's oscillation, as determined from the graph, is 0.7 seconds.

### How is the spring constant k calculated in the experiment?

-The spring constant k is calculated using the formula for the period of a simple harmonic oscillator, which is T = 2 * pi * sqrt(m/k), where T is the period and m is the mass of the block. By rearranging and solving for k, and substituting the given values, the spring constant is found to be 24 Newtons per meter.

### What are the forces acting on the block when it is moving towards the equilibrium position on a rough surface?

-When the block is moving towards the equilibrium position on a rough surface, the forces acting on it include the gravitational force pulling it down, the normal force exerted by the table upwards, the spring force pushing it to the right, and the kinetic frictional force acting to the left.

### How should the free body diagrams be drawn according to the script?

-The free body diagrams should be accurate depictions of the forces acting on the block, with each force represented by a distinct arrow starting from the dot and pointing away from it. Forces in the same direction should not be drawn on top of each other or touching.

### What changes in the velocity versus time graph when the block is on a rough surface compared to an ideal surface?

-On a rough surface, the velocity versus time graph will still show sinusoidal oscillations, but the amplitude of the oscillations will decrease over time due to friction, while the period remains constant.

### What is the importance of practicing free response questions as mentioned in the script?

-Practicing free response questions is important as it helps in better understanding of the concepts and improves the chances of scoring well on the AP exam.

###### Outlines

00:00

##### 📚 Introduction to AP Physics Daily Practice on Simple Harmonic Motion

Dee Dee Messer, an AP Physics teacher, introduces a session focused on simple harmonic motion for AP Physics students. She provides an option to download a PDF of the question or to pause the video to work through the problem. The session begins with a scenario involving a 0.3 kg block attached to a spring on a table, set into motion by stretching the spring. A motion detector records the block's position, resulting in a velocity versus time graph. The positive direction is established as to the right, and students are guided to derive an expression for velocity, including numerical values for all constants, from the given simple harmonic motion equation.

05:00

##### 🔍 Deriving Velocity Expression and Analyzing Scoring Guidelines

The instructor derives the expression for velocity as the derivative of the position function, which is given by the maximum displacement times cosine of omega times time. She uses the graph to find the maximum velocity and the period of the motion to substitute into the expression, resulting in a numerical value for velocity. The scoring guidelines for this part are explained, emphasizing the importance of the trigonometric expression, the correct use of the period to find omega, and the range for the maximum speed. The summary also includes the process of deriving the position function from the velocity function by integration.

10:01

##### 🔧 Calculating Spring Constant and Understanding Free Body Diagrams

The session continues with calculating the spring constant 'k' using the period and mass from the previous parts. The formula relating the period to the spring constant is derived and solved for 'k', yielding a numerical value. The scoring guidelines for this calculation are reviewed, highlighting the correct use of the formula and consistent substitution of values. The second part of the session involves a new experiment on a rough surface, where students are asked to draw and label the forces acting on the block when it is at two different positions and moving in specified directions, emphasizing the importance of accurate free body diagrams.

##### 📉 Sketching Damped Oscillation and Concluding the Session

The final part of the video script discusses part e, which involves sketching the velocity versus time graph for damped oscillation on a rough surface, assuming negligible change in the period. The instructor explains that the graph should still show sinusoidal motion but with decreasing amplitude due to friction. The scoring for this part is based on the graph correctly showing the period, the damping effect, and the initial direction of motion. The video concludes with encouragement for students to practice regularly for better AP exam results and a wish for good luck on the exam day.

###### Mindmap

###### Keywords

##### 💡Simple Harmonic Motion

Simple Harmonic Motion (SHM) refers to the motion of an object when it moves back and forth over the same path within a stabilizing, restoring force proportional to the displacement. In the context of the video, SHM is the central theme, as the block attached to a spring undergoes oscillatory motion. The video script describes how to derive expressions for velocity and position based on SHM, using the cosine function to represent the motion.

##### 💡Velocity

Velocity is a vector quantity that represents the rate of change of an object's position with respect to time. In the video, the teacher explains how to derive an expression for velocity in SHM by taking the derivative of the position function with respect to time. The velocity expression is crucial for understanding how fast the block is moving at any given moment during its oscillation.

##### 💡Derivative

The derivative in calculus is a measure of how a function changes as its input changes. In the script, the teacher uses the derivative to find the velocity of the block by differentiating the position function. This mathematical operation is fundamental in physics for relating displacement to velocity in SHM.

##### 💡Spring Constant (k)

The spring constant, denoted as 'k', is a measure of the stiffness of a spring. It is the proportionality constant in Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from the equilibrium position. The video script includes a calculation of the spring constant using the period of oscillation and the mass of the block.

##### 💡Period

The period of a motion is the time taken for one complete cycle of the motion to occur. In SHM, the period is used to calculate the angular frequency and is essential for understanding the time it takes for the block to complete one oscillation. The video script mentions finding the period from a velocity-time graph.

##### 💡Angular Frequency (ω)

Angular frequency, symbolized by ω, is a measure of how fast an object undergoes SHM, expressed in radians per second. It is related to the period of the motion by the formula ω = 2π/T. In the video, the teacher uses angular frequency in the velocity expression for SHM and calculates it using the period found from the graph.

##### 💡Damping

Damping refers to the reduction in amplitude of an oscillating system due to the effects of friction or other resistive forces. In the script, the second experiment introduces a rough surface, which causes the oscillations to damp over time, reducing the amplitude of the block's motion without changing the period.

##### 💡Amplitude

Amplitude is the maximum displacement of the oscillating object from its equilibrium position. In the context of the video, the amplitude of the block's motion decreases due to damping forces when the system is placed on a rough surface, illustrating the effect of non-ideal conditions on SHM.

##### 💡Free Body Diagram

A free body diagram is a graphical representation that shows all the forces acting on an object in a particular situation. In the script, the teacher instructs how to draw free body diagrams for the block in two different scenarios, illustrating the forces of gravity, normal force, spring force, and friction.

##### 💡Frictional Force

Frictional force is the force that opposes the motion of an object when it is in contact with another surface. In the video, the teacher explains how frictional force acts on the block when it is placed on a rough surface, affecting the block's motion and leading to damping of the oscillations.

##### 💡Equilibrium Position

The equilibrium position is the position where the net force on an object is zero, and there is no tendency for the object to move in any direction. In SHM, this is the central position between the maximum displacements. The video script discusses how the forces acting on the block change depending on whether it is moving towards or away from the equilibrium position.

###### Highlights

Introduction to the AP Physics Daily Practice video session focused on simple harmonic motion.

Option to download a PDF of the question or pause the video to work through the problem.

Experiment setup with a 0.3 kg block attached to a spring on a horizontal table.

Use of a motion detector to record the block's position during oscillation.

Derivation of an expression for velocity in simple harmonic motion, including numerical values for constants.

Explanation of the importance of the direction of positive and negative values in the context of the problem.

Integration of velocity to derive the position function of the block as a function of time.

Calculation of the spring constant k using the period of oscillation and mass of the block.

Demonstration of how to draw and label forces acting on the block in two different scenarios on a rough surface.

Emphasis on the accuracy and clarity of free body diagrams in understanding the forces involved.

Scoring guidelines for deriving expressions and drawing diagrams, highlighting the importance of consistency and accuracy.

Introduction of a second experiment with the block and spring on a rough surface, affecting the motion.

Instructions on drawing velocity versus time graphs for damped oscillations with a rough surface.

Assumption of negligible change in the period despite the presence of friction.

Sketching a graph to illustrate the effect of friction on amplitude while maintaining a constant period.

Scoring details for the velocity versus time graph, emphasizing the importance of the graph's features.

Conclusion of the video with a summary of the 15 points covered in the free response question.

Encouragement for viewers to practice regularly for better results on the AP exam.

###### Transcripts

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AP PhysicsMechanicsDaily PracticeFree ResponseSimple Harmonic MotionVelocityPositionSpring ConstantFrictionDamping OscillationEducational Video