2023 AP Physics 1 Free Response #2

Allen Tsao The STEM Coach
13 May 202314:12
EducationalLearning
32 Likes 10 Comments

TLDRIn this educational video, the presenter tackles FRQ2 from the 2023 AP Physics 1 exam, offering a step-by-step analysis to determine the acceleration of a cart rolling down a ramp. They suggest graphing position versus one-half time squared to obtain a straight line, the slope of which represents acceleration. The video also covers calculating the experimental value of gravity, considering the angle of the ramp, and discusses potential discrepancies due to factors other than friction or air resistance. Finally, it explores confirming acceleration consistency whether the cart rolls up or down the ramp, sketching position and velocity over time for both scenarios.

Takeaways
  • 📝 Students conduct an experiment to determine the acceleration of cart A, released from rest at the top of a ramp.
  • 📈 To determine acceleration, plot position versus time using the kinematic equation x = (1/2)at^2.
  • 🔢 Calculate and plot the quantities needed for a straight line graph, where the slope represents acceleration.
  • 📊 Properly label graph axes with position (meters) on the vertical axis and (1/2)t^2 (seconds squared) on the horizontal axis.
  • 🖊️ Draw a straight line through the plotted points to determine the slope, representing the acceleration.
  • 📐 Use the graph to calculate the experimental value of acceleration and then determine the experimental value of gravity.
  • 🌡️ To calculate gravity, consider the angle of the ramp and use the relationship a = g sin(θ).
  • ⚖️ Discuss potential errors in measurement, such as the miscalculated angle or additional external forces.
  • 📉 Consider reasons for a lower experimental value of gravity, excluding friction and air resistance.
  • 🔄 Sketch position and velocity graphs for the cart rolling up and down the ramp, highlighting the quadratic nature of the motion and the impact of acceleration.
Q & A

  • What is the main objective of the experiment described in the script?

    -The main objective of the experiment is to determine the acceleration of a cart as it moves down a ramp from rest.

  • What is the initial velocity of the cart when it is released from rest?

    -The initial velocity of the cart is zero because it is released from rest at the top of the ramp.

  • Which kinematic equation is used to relate the variables in the experiment?

    -The kinematic equation used is x = (1/2)at^2, where x is the displacement, a is the acceleration, and t is the time.

  • Why is it important to graph position versus (1/2)t^2 instead of just time?

    -Graphing position versus (1/2)t^2 yields a straight line whose slope can be used to determine the acceleration of the cart directly, as the slope represents the acceleration.

  • What should be the units for the vertical and horizontal axes when plotting the graph?

    -The vertical axis should have meters for the position unit, and the horizontal axis should have seconds squared for the (1/2)t^2 unit.

  • How does the experimenter calculate the acceleration of the cart from the graph?

    -The acceleration is calculated from the graph by determining the slope of the straight line, which is the change in position divided by the change in (1/2)t^2.

  • What additional quantity is needed to calculate the experimental value of gravity (Gx) from the acceleration?

    -To calculate Gx, the angle of the ramp (Theta) is needed, as the acceleration is G sine Theta on an inclined plane.

  • Why might the experimental value of Gx be significantly lower than the accepted value of 9.8 m/s^2?

    -The experimental value of Gx might be lower if the angle of the ramp is mismeasured, resulting in an overestimation of sine Theta, or if there is an external force acting on the cart that reduces the acceleration.

  • How can students confirm that the acceleration is the same whether the cart rolls up or down the ramp?

    -Students can confirm the acceleration's consistency by starting the cart at the bottom, giving it a push to roll up the ramp, and observing the motion momentarily coming to rest, indicating the same acceleration in both directions.

  • What is the expected shape of the position and velocity graphs when the cart moves up the ramp?

    -The position graph is expected to be a parabola, and the velocity graph will show a negative slope initially, going through zero, and then a positive slope as the cart slows down, momentarily comes to rest, and then rolls back down.

Outlines
00:00
📊 Analyzing Acceleration in AP Physics 1

The video discusses the second free-response question (FRQ2) from the 2023 AP Physics 1 exam, focusing on determining the acceleration of a cart released from rest on a ramp. The key concepts include kinematics, the relationship between position and time, and how to graph data to yield a straight line to determine acceleration. The speaker explains the kinematic equation x = (1/2)at^2 and how to plot position versus (1/2)t^2 to find acceleration. Calculations for (1/2)t^2 values and plotting them on a graph are detailed, along with finding the slope to determine acceleration.

05:00
📐 Determining Experimental Gravity

The speaker moves on to using the experimental acceleration to calculate the gravitational constant g. They explain that the acceleration a can be used in the equation a = g sin θ where θ is the ramp angle. They discuss the importance of accurately measuring θ and potential reasons for discrepancies in experimental results. If the angle θ is mismeasured, it can significantly impact the calculated value of g. They also touch upon other potential forces that could affect the cart's acceleration, beyond just friction and air resistance.

10:02
🔄 Velocity and Position Graphs for Cart Movement

The final part of the video discusses the behavior of the cart as it moves up and down the ramp after being given a push. The position-time graph for the cart is described as a parabola, showing initial movement up the ramp, coming to rest, and then moving back down. The corresponding velocity-time graph starts with a negative velocity, reaches zero at the highest point of the ramp, and then increases positively as the cart moves down. The explanation emphasizes the quadratic nature of the position equation and how the velocity changes in relation to the position graph.

Mindmap
Keywords
💡Acceleration
Acceleration refers to the rate at which an object's velocity changes over time. In the context of the video, it is a crucial variable that the students are trying to determine for a cart moving down a ramp. The video explains how acceleration can be derived from the slope of a graph plotting position versus time squared.
💡Kinematics
Kinematics is the branch of mechanics that describes the motion of objects without considering the causes of that motion. The video discusses kinematic equations to relate variables such as displacement, initial velocity, acceleration, and time, which are essential for analyzing the cart's motion down the ramp.
💡Position vs. Time Graph
A position vs. time graph plots an object's position along the vertical axis and time along the horizontal axis. In the video, such a graph is used to determine the acceleration of the cart by analyzing the slope of the line, which, when plotted with position and time squared, should yield a straight line if the motion is uniformly accelerated.
💡Slope
The slope of a graph represents the rate of change between the two variables plotted. In the video, the slope of the position vs. half time squared graph is used to determine the cart's acceleration. A steeper slope indicates a higher acceleration.
💡Initial Velocity
Initial velocity is the velocity of an object at the start of a time interval. In the video, the cart's initial velocity is zero since it starts from rest at the top of the ramp, which simplifies the kinematic calculations.
💡Kinematic Equation
A kinematic equation is a mathematical formula that relates the variables of motion. The video uses the kinematic equation x = 1/2at^2 to describe the relationship between position, acceleration, and time for the cart moving down the ramp.
💡Gravity
Gravity is the force that attracts objects toward the center of the Earth, causing them to accelerate downwards. The video explains how the acceleration of the cart is related to the gravitational constant (g) and the angle of the ramp via the equation a = g*sin(theta).
💡Inclined Plane
An inclined plane is a flat surface tilted at an angle to the horizontal. The cart in the video moves down an inclined plane, and its motion is analyzed to determine the acceleration due to gravity along the ramp's surface.
💡Free Body Diagram
A free body diagram is a graphical illustration used to visualize the forces acting on an object. In the video, a free body diagram of the cart on the inclined plane helps explain how the gravitational force is decomposed into components parallel and perpendicular to the ramp.
💡Experimental Error
Experimental error refers to the deviation of the experimental result from the true value. The video discusses potential sources of error in measuring the acceleration of the cart, such as mismeasuring the angle of the ramp or other external forces not accounted for in the simple model.
Highlights

Students conduct an experiment to determine the acceleration of cart A.

The cart is released from rest at the top of the ramp, and the x-axis is defined to be parallel to the ramp.

To determine acceleration, the students use the kinematic equation x = 1/2at².

For a straight-line graph, the vertical axis should be position (x) and the horizontal axis should be 1/2t².

The slope of the position vs. 1/2t² graph will give the acceleration.

Computed values of 1/2t² for various time points are calculated to plot the graph.

The axes of the graph are labeled with appropriate units: position in meters and 1/2t² in seconds².

Data points are plotted on the graph and a straight line is drawn to fit the points.

Two points on the graph are chosen to calculate the slope, which represents the acceleration.

To determine the experimental value of gravity, additional quantities such as the angle of the ramp need to be measured.

The acceleration of the cart can be related to gravity using the equation a = g sin(θ).

Possible reasons for the experimentally determined value of g being significantly lower than 9.8 m/s² are discussed, excluding friction and air resistance.

Other external forces or measurement inaccuracies in the angle of the ramp could cause deviations.

Students also test if the acceleration is consistent when the cart is pushed up the ramp.

Graphs of position and velocity as functions of time are sketched for the cart moving up and down the ramp.

Transcripts

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Physics ExperimentAccelerationKinematicsCart MotionRamp AngleTime MeasurementVelocity GraphEducational ContentScience EducationExperiment AnalysisMismeasurement Issue