2021 AP Physics 1 Free Response #5 (First Administration)
TLDRIn this educational video, the presenter tackles a 2021 AP Physics 1 free response question involving a system of two pulleys with different radii and objects of varying masses attached. The task is to derive an expression for the net torque on the system after release from rest. The video explains the concept of torque, the direction of angular acceleration, and the effects of cutting the string on the system's motion. It also includes a discussion on sketching a graph of angular velocity over time, considering the entire interval from release to string cut.
Takeaways
- ๐ง The video discusses a physics problem involving two pulleys of different radii attached to a horizontal axle with negligible friction.
- ๐ The problem is from the 2021 AP Physics 1 free response section, and the presenter acknowledges potential mistakes will be noted in the description.
- ๐ The system consists of two objects with masses m0 and 1.5m0 hanging from strings wrapped around the pulleys, with m0 being the mass of object one.
- ๐ The pulleys are released from rest, and the objects begin to accelerate, creating a net torque on the system about the axle.
- ๐งญ The direction of the net torque is initially counterclockwise, causing object one to accelerate downward due to the heavier mass of object two.
- ๐ The magnitude of the net torque is derived to be 0.5 * r0 * m0 * g, where r0 is the radius of the larger pulley.
- ๐ After the string of object one is cut at time tc, the net torque direction changes to clockwise, causing the system to decelerate.
- ๐ The angular velocity and angular acceleration of the pulley system are compared after the string is cut, indicating they are in opposite directions.
- ๐ A graph of angular velocity as a function of time is sketched, showing the change in slope at time tc when the string is cut.
- ๐ข The slope of the angular velocity graph changes from one over three before tc to a positive one after tc, reflecting the change in net torque.
- ๐ The presenter emphasizes the importance of establishing the correct direction for torque and acceleration in the analysis of the system.
Q & A
What is the scenario described in the 2021 AP Physics 1 free response question?
-The scenario involves two pulleys with different radii attached to each other, rotating along a horizontal axle with negligible friction. Object one hangs from a light string around a large pulley, and object two hangs from another light string around a smaller pulley. The system is released from rest, and the task is to derive an expression for the net torque on the system.
What are the given physical constants and variables in the problem?
-The given constants and variables are the mass of object one (m0), the mass of object two (1.5m0), the radius of the smaller pulley (r0), and the radius of the larger pulley (2r0).
What is the initial condition of the system when the pulleys are released?
-The initial condition is that the pulleys are released from rest, meaning the initial angular velocity is zero.
Why does object one accelerate downward after the pulleys are released?
-Object one accelerates downward because the net torque on the system is in the counterclockwise direction, causing the system to rotate counterclockwise, which results in object one moving downward.
What is the expression for the net torque on the system derived in the script?
-The derived expression for the net torque is 0.5 * r0 * m0 * g, where g is the acceleration due to gravity.
What happens to the system when the string of object one is cut at time tc?
-When the string of object one is cut, the net torque becomes positive (clockwise direction), and the system, which was initially rotating counterclockwise, starts to slow down.
How do the directions of angular velocity and angular acceleration compare after the string is cut?
-After the string is cut, the angular velocity remains counterclockwise, but the angular acceleration changes to the clockwise direction, as the net torque is now in the clockwise direction.
What is the significance of the torque direction in the rotation of the pulleys?
-The direction of the torque determines the direction of the angular acceleration and thus the rotation of the pulleys. A positive torque (clockwise) will cause a positive angular acceleration, while a negative torque (counterclockwise) will cause a negative angular acceleration.
How does the net torque change the system's angular velocity over time?
-The net torque causes the system's angular velocity to change according to the torque's magnitude and direction. Initially, a net torque of 0.5 * r0 * m0 * g causes a counterclockwise rotation, and after the string is cut, the net torque increases to 1.5 * r0 * m0 * g, resulting in a change in the angular velocity's rate of change.
What is the task of sketching a graph of angular velocity as a function of time?
-The task is to sketch a graph showing how the angular velocity of the system changes over time, including the entire time interval from when the pulleys are released (t0) to when the string is cut (tc).
What is the relationship between the net torque and the angular acceleration of the system?
-The net torque is directly proportional to the angular acceleration of the system. According to Newton's second law for rotation, the net torque equals the moment of inertia times the angular acceleration (ฯ = I * ฮฑ).
Outlines
๐ง Mechanics of Pulley Systems and Torque Analysis
This paragraph discusses a physics problem involving two pulleys of different radii connected by a horizontal axle with negligible friction. The problem describes a scenario where two objects with masses m0 and 1.5m0 are hanging from strings wrapped around the pulleys. Upon release, the system begins to accelerate, and the task is to derive an expression for the net torque exerted on the system about the axle. The speaker initially outlines the forces acting on the objects and the concept of tension in the strings, then moves on to calculate the net torque considering the system as a whole. The torque from object one is positive, causing clockwise rotation, while the torque from object two is negative, causing counterclockwise rotation. The net torque is determined to be negative, indicating counterclockwise rotation, and is expressed in terms of m0, r0, and gravitational acceleration.
๐ Angular Dynamics Post-Release and String Cutting
The second paragraph delves into the dynamics of the pulley system after the initial release and subsequent cutting of the string of object one. The net torque direction is explained to be counterclockwise, which corresponds to the angular acceleration of the system. When the string is cut at time tc, the only remaining torque is in the clockwise direction, causing the system to slow down its counterclockwise spin. The angular velocity and angular acceleration are in opposite directions at this point. The speaker then sketches a graph of angular velocity over time, indicating the change in slope representing the change in angular acceleration before and after the string is cut, with the slope being inversely proportional to the net torque acting on the system.
๐ Graphing Angular Velocity Over Time
In the final paragraph, the focus is on graphing the angular velocity of the pulley system as a function of time. The speaker outlines the process of graphing, considering the entire time interval from the release of the pulleys at t0 to the cutting of the string at tc. Initially, the angular velocity is negative, indicating counterclockwise motion. The net torque before tc is calculated, and after tc, the torque changes, resulting in a different slope on the graph. The speaker emphasizes the importance of the direction of torque and its effect on the system's angular acceleration, leading to a change in the graph's slope from one-third to one, reflecting the system's transition from acceleration to deceleration.
Mindmap
Keywords
๐กAP Physics
๐กPulleys
๐กTorque
๐กNet Torque
๐กFree Body Diagram
๐กTension
๐กAcceleration
๐กAngular Acceleration
๐กGraph
๐กCutting the String
Highlights
Introduction to the 2021 AP Physics 1 free response question on pulleys and torque.
Description of the problem setup involving two pulleys with different radii and objects attached.
Assumption of negligible friction on the axle for simplification.
Explanation of the forces acting on the system and the initial conditions.
Identification of the need for a free body diagram to analyze the system.
Discussion on the direction of acceleration and the forces involved in the system.
Differentiation between internal and external forces in the pulley system.
Calculation of torque considering the radius and mass of the objects.
Derivation of the net torque exerted on the pulley system after release.
Misinterpretation of the torque direction and subsequent correction.
Explanation of why object one accelerates downward after the pulleys are released.
Discussion on the angular velocity and acceleration of the pulleys after the string is cut.
Analysis of the change in torque direction and its effect on angular velocity and acceleration.
Sketching a graph of angular velocity as a function of time, including the effect of the string being cut.
Explanation of the slope changes in the graph representing the angular velocity over time.
Final review of the problem-solving process and the steps taken to derive the solution.
Transcripts
Browse More Related Video
5.0 / 5 (0 votes)
Thanks for rating: