AP Physics 2023 Exam Solutions|Q2. PART A ( ii) | Complete Step-by-Step Answers and Explanations"

Study Circus
10 Oct 202304:47
EducationalLearning
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TLDRThe second part of the question involves plotting a graph to determine the acceleration of a cart coming down an incline. By labeling the axes and plotting the points, a straight line passing through the origin is obtained, where the x-axis represents t²/2 and the y-axis represents the position. The slope of the line, calculated using two points, gives the experimental acceleration of the cart as 1.22 m/s². This value is derived from the data plotted on the graph.

Takeaways
  • 📈 The task involves the second part of a physics problem concerning the acceleration of a cart moving down an incline.
  • 📚 The first part of the question has already been completed, and this script addresses the second part, focusing on graph plotting.
  • 📏 The positive x-direction is chosen along the incline, with the cart's movement considered positive in the x-direction.
  • 📊 The script instructs to plot the graph with 'x' as the independent variable and the position 'X' as the dependent variable.
  • 📉 The equation of motion given is X = (1/2)at², which simplifies to X = at²/2 for plotting purposes.
  • 📍 The script describes the process of plotting points based on the provided data and drawing a straight line that passes through the origin.
  • 📌 The slope of the straight line graph represents the acceleration 'a' of the cart.
  • 🔍 The script details the method of finding the slope by selecting two points on the line and calculating the change in y divided by the change in x.
  • 📝 The experimental value of acceleration 'a' is calculated to be 1.22 m/s² by using the slope of the graph.
  • 🔢 The process involves mathematical operations such as subtraction and division to find the slope and, consequently, the acceleration.
  • 🎓 The script concludes by summarizing the method used to determine the acceleration of the block rolling down the incline using a graphical approach.
Q & A

  • What is the second part of question 2 in the transcript about?

    -The second part of question 2 is about plotting the appropriate quantities on a graph to determine the acceleration 'a' of a cart coming down an incline.

  • What was the chosen positive X direction in the experiment?

    -The positive X direction was chosen to be along the incline, in the direction the cart was moving.

  • What mathematical equation is being plotted on the graph?

    -The equation being plotted is X = (1/2)at², where X is the position along the incline and t is time.

  • What are the independent and dependent variables in the graph?

    -The independent variable is time squared (t²), and the dependent variable is the position X along the incline.

  • How is the acceleration 'a' represented on the graph?

    -The acceleration 'a' is represented as the slope of the straight line graph that passes through the origin.

  • What is the significance of the straight line passing through the origin in the graph?

    -The straight line passing through the origin indicates that the initial velocity of the cart is zero, and the motion is uniformly accelerated from rest.

  • How many points are used to plot the graph in the transcript?

    -Four points are used to plot the graph, corresponding to different time intervals and positions of the cart.

  • What is the method to calculate the experimental value of acceleration 'a'?

    -The experimental value of acceleration 'a' is calculated by finding the slope of the straight line graph, which is the change in position divided by the change in time squared.

  • What are the two points chosen to calculate the slope of the line in the transcript?

    -The two points chosen are (0.24, 0.174) and (0.14, 0.296), which correspond to different values of time squared and position.

  • What is the calculated acceleration of the block as it rolls down the incline?

    -The calculated acceleration of the block is 1.22 m/s², obtained by finding the slope of the graph.

  • How does the transcript ensure the graph accurately represents the experimental data?

    -The transcript ensures accuracy by plotting the data points, connecting them with a straight line, and then calculating the slope of this line to find the acceleration.

Outlines
00:00
📈 Graphing Acceleration Data

The script describes the process of plotting data to determine the acceleration 'a' of a cart moving down an incline. The cart's position along the incline is represented on the y-axis against time squared divided by two on the x-axis. The graph is expected to be a straight line passing through the origin, with the slope representing the acceleration. Key points from the data are identified and plotted, resulting in a linear graph that visually represents the motion of the cart.

🧭 Calculating Acceleration from the Graph

The second part of the script focuses on calculating the experimental value of acceleration 'a' using the graph plotted in the first part. The slope of the line is determined by selecting two points on the graph and calculating the change in y over the change in x. The specific points chosen are (0.24, 0.174) and (0.296, 0.14), and the slope calculation simplifies to 1.22. This value is interpreted as the acceleration of the block as it rolls down the incline, expressed in meters per second squared (m/s²).

Mindmap
Keywords
💡acceleration
Acceleration refers to the rate of change of velocity of an object. In the script, it is the primary quantity being determined as the cart moves down the incline. The slope of the graph representing position versus time squared helps calculate the cart's acceleration.
💡incline
An incline is a sloped surface or ramp. The script describes an experiment where a cart moves down an inclined plane, with the positive x-direction being along the slope. The incline is crucial for understanding the motion and the forces acting on the cart.
💡graph
A graph is a visual representation of data. In the script, a graph is plotted with time squared divided by 2 on the x-axis and position on the y-axis. The graph helps determine the acceleration by finding the slope of the line that best represents the data points.
💡slope
The slope of a graph indicates the rate of change between the variables on the x and y axes. In the context of the script, the slope of the line on the graph represents the acceleration of the cart. It is calculated by dividing the change in position by the change in time squared.
💡position
Position refers to the location of an object at a particular point in time. In the script, position is plotted on the y-axis of the graph to study the motion of the cart. The position data points help in determining the relationship between time and displacement.
💡t²/2
t²/2 represents half of the time squared, which is used as the independent variable on the x-axis of the graph in the script. This quantity is essential for creating a linear relationship with position, allowing for the determination of acceleration.
💡data points
Data points are individual values that represent the relationship between two variables. In the script, data points are marked on the graph to visualize the cart's position at different times. Connecting these points helps in forming the line whose slope is used to find acceleration.
💡experimental value
An experimental value is a quantity obtained through observation and measurement during an experiment. In the script, the experimental value of the cart's acceleration is determined by analyzing the slope of the line on the graph derived from the data points.
💡straight line
A straight line on a graph indicates a constant relationship between the variables. In the script, the straight line passing through the origin on the position versus time squared graph signifies a constant acceleration, allowing for straightforward calculation of the slope.
💡origin
The origin is the point (0,0) on a graph where the x and y axes intersect. In the script, the straight line passes through the origin, indicating that the position of the cart is directly proportional to the square of the time, which simplifies the calculation of acceleration.
Highlights

Introduction of the second part of question 2, a continuation from the first part.

Description of the cart's motion down an incline and the positive X direction chosen for analysis.

Explanation of the graph's axes labeling and scaling for plotting data.

The mathematical relationship X = 1/2 * at² is established for plotting.

Identification of the independent variable (time squared) and the dependent variable (position).

The slope of the graph represents the acceleration 'a' of the cart.

Plotting of points based on the given data to create a straight line graph.

The graph is expected to be a straight line passing through the origin, indicating a direct relationship.

Marking specific points from the data to be plotted on the graph.

Connecting the dots to visualize the straight line representing the cart's acceleration.

Calculation of the experimental value of acceleration 'a' using the slope of the plotted line.

Selection of two points on the graph to calculate the slope and thus the acceleration.

Mathematical computation to find the slope and acceleration, resulting in a value of 1.22 m/s².

Conclusion of the second part of the question with the experimental value of acceleration.

Acknowledgment of the completion of part two and transition to the third part of the question.

The practical application of the graph in determining the acceleration of an object in motion.

The importance of accurate data plotting for reliable experimental results.

The methodological approach to solving physics problems using graphical analysis.

Transcripts

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Related Tags
PhysicsAccelerationCart MotionGraph AnalysisIncline SlopeExperimentData PlottingSlope CalculationM/s²Educational