2016 #1 Free Response Question - AP Physics 1 - Exam Solution
TLDRIn this educational video, the hosts tackle a free response question from the 2016 AP Physics 1 exam, which involves analyzing a wooden wheel rolling down an inclined ramp. The discussion covers the forces acting on the wheel, such as gravity, normal force, and static friction, and their impact on the wheel's motion and angular velocity. The video emphasizes the importance of free body diagrams in problem-solving and provides a detailed breakdown of how to calculate the linear acceleration of the wheel's center of mass given the ramp's angle and the force of friction. Additionally, a comparison is made between the wheel and a block of ice sliding down the ramp, examining which reaches the bottom with greater speed using both force and energy principles.
Takeaways
- 📚 The video discusses free response question #1 from the 2016 AP Physics 1 exam, focusing on a wooden wheel rolling down an inclined ramp.
- 🎨 In part (a)i, students are instructed to draw a free body diagram labeling the forces acting on the wheel, including gravity, normal force, and static friction.
- 🔽 The wheel's center of mass experiences gravity, normal force perpendicular to the ramp, and static friction parallel to the ramp and up it.
- 🌀 Part (a)ii asks which force causes a change in the wheel's angular velocity, with the answer being the static friction force, as it's the only one causing a net torque.
- 📈 In part (b), students derive an expression for the wheel's linear acceleration, considering the force of friction as 40% of the maximum static friction force.
- 🔄 The wheel's acceleration is calculated using Newton's Second Law and the components of gravitational force, resulting in 0.6 times the gravitational acceleration times the sine of the ramp angle.
- 🧊 Part (c) introduces a second experiment with an ice block sliding down the ramp with negligible friction, compared to the wheel rolling down.
- 🏎️ For part (c)i, the block with no friction reaches the bottom with a greater speed than the wheel, due to a larger acceleration down the incline.
- 🌐 In part (c)ii, both the block and the wheel start with the same gravitational potential energy, but the block has more translational kinetic energy at the bottom due to lack of rotation.
- 💯 The video emphasizes the importance of free body diagrams in problem-solving, as they account for a significant portion of the exam points.
- 📝 When answering exam questions, explanations are crucial and must be provided; failure to do so often results in zero points.
- 📚 The grading guidelines allow for points in part (b) even if part (a) is incorrect, as long as the solution to part (b) is mathematically sound.
Q & A
What is the main topic of the video?
-The main topic of the video is solving free response question #1 from the 2016 AP Physics 1 exam, which involves analyzing a wooden wheel rolling down a ramp under the influence of various forces.
What are the forces acting on the wheel as it rolls down the ramp?
-The forces acting on the wheel include gravity acting at the center of mass, the normal force at the point of contact with the ramp, and the static friction force parallel to the ramp and up the incline.
How is the force of static friction related to the wheel rolling without slipping?
-The force of static friction opposes the motion that would cause the wheel to slide down the ramp. It acts parallel to and up the incline at the point of contact, allowing the wheel to roll without slipping.
What is the significance of the free body diagram in solving this problem?
-The free body diagram is crucial for visualizing all the forces acting on the wheel and is worth 2 out of 7 points in the exam. It helps in understanding the forces and their directions, which is essential for solving the problem correctly.
Which force causes a change in the angular velocity of the wheel?
-The force of static friction causes a change in the angular velocity of the wheel because it is the only force that creates a net torque about the center of mass of the wheel.
How is the linear acceleration of the wheel's center of mass derived in part (b) of the problem?
-The linear acceleration of the wheel's center of mass is derived by summing the forces in the parallel direction (down the incline) and applying Newton's second law (F_net = m*a). The force of static friction is 40% of the force of gravity parallel to the incline, leading to an acceleration of 0.6 times the acceleration due to gravity times the sine of the incline angle.
What is the difference between the wheel and the block in the second experiment described in part (c)?
-In the second experiment, the wheel has a force of static friction acting on it, while the block of ice has negligible friction. This difference in forces leads to different accelerations and ultimately different speeds at the bottom of the ramp.
Which object reaches the bottom of the ramp with the greatest speed, and why?
-The block reaches the bottom of the ramp with the greatest speed because it has no friction acting on it, leading to a larger acceleration and thus a higher speed at the bottom compared to the wheel, which has to expend some of its energy on rotation.
How does the concept of energy explain the difference in speed between the wheel and the block?
-Both the wheel and the block start with the same amount of gravitational potential energy. However, as they move down the ramp, the wheel has to distribute some of its energy into rotational kinetic energy, while the block converts all its potential energy into translational kinetic energy, resulting in a higher speed for the block.
What is the importance of providing explanations in the exam?
-Providing explanations is crucial in the exam as it demonstrates the student's understanding of the concepts. The College Board awards points for both the correct answer and a proper explanation, emphasizing the need for a clear and comprehensive understanding of the physics involved.
What is the grading guideline for part (b) regarding the force diagram in part (a)?
-The expression in part (b) need not be correct or consistent with the force diagram in part (a). Students can still earn points for part (b) even if their solution is based on an incorrect part (a), as long as the solution to part (b) is correct.
What is the expected format for answers in the AP Physics 1 exam?
-The College Board expects answers to be in terms of the variables provided in the problem, such as mass, incline angle, and physical constants. Answers should not include other variables like the coefficient of static friction, and numerical values for fundamental constants like gravity should not be substituted.
Outlines
📚 Physics Exam Question Analysis: Rolling Wheel on a Ramp
This paragraph discusses the process of solving a free response question from the 2016 AP Physics 1 exam. The scenario involves a wooden wheel rolling down an inclined ramp, and students are tasked with identifying and diagramming the forces acting on the wheel. The key forces include gravity, normal force, and static friction. The importance of free body diagrams in problem-solving is emphasized, as they account for a significant portion of the exam's scoring. The paragraph also covers the rationale behind the wheel's angular velocity change, attributing it to the net torque caused by static friction. Additionally, a detailed explanation is provided for deriving the linear acceleration of the wheel's center of mass, given the ramp's angle and the force of friction.
🚀 Comparing Rolling Wheel and Sliding Block: Speed and Energy Perspectives
In this paragraph, the discussion shifts to a second experiment involving both a rolling wheel and a sliding block on the same inclined ramp. The focus is on determining which object reaches the bottom with the greatest speed, considering the forces and energy transformations involved. The block, lacking friction, experiences a greater acceleration and thus a higher speed at the bottom. The explanation is further deepened by considering the energy perspective, where the block's lack of rotation means all its gravitational potential energy is converted into translational kinetic energy, unlike the wheel, which also has rotational kinetic energy. The importance of providing explanations in exams is stressed, with a reminder that unexplained answers are likely to receive zero points.
Mindmap
Keywords
💡Free Body Diagram
💡Center of Mass
💡Static Friction
💡Angular Velocity
💡Newton's Second Law
💡Acceleration Due to Gravity
💡Incline Angle
💡Rotational Inertia
💡Kinetic Energy
💡Gravitational Potential Energy
Highlights
The problem-solving session focuses on free response question #1 from the 2016 AP Physics 1 exam.
The scenario involves a wooden wheel rolling down an inclined ramp, with the forces acting on the wheel being the subject of analysis.
The wheel experiences gravity, normal force, and static friction as it rolls without slipping.
The importance of free body diagrams in physics problem-solving is emphasized, with 30% of the points in this problem coming from the diagram.
The force of static friction is identified as the cause of the change in angular velocity of the wheel.
An expression for the linear acceleration of the wheel's center of mass is derived using principles of Newton's Second Law and torque.
The block of ice, in a second experiment, slides down the ramp with negligible friction compared to the wheel.
The block with no friction reaches the bottom with a greater speed due to a larger acceleration down the incline.
Both the block and the wheel start with the same amount of mechanical energy, which is converted to kinetic energy as they descend.
The block has more translational kinetic energy than the wheel because the wheel also has rotational kinetic energy.
The grading guidelines specify that explanations are mandatory for scoring, emphasizing the need for full sentences in responses.
The problem-solving process highlights the application of fundamental physics concepts such as force analysis, Newton's Laws, and energy conservation.
The session underscores the practical application of theoretical physics in real-world scenarios, like the rolling wheel and sliding block.
The problem-solving approach demonstrates the step-by-step method of tackling physics problems, which is beneficial for students preparing for exams.
The transcript serves as an educational resource, providing insights into the thought process and methodology behind solving physics problems.
The session's interactive format, with different participants reading and answering parts of the problem, models a collaborative learning environment.
The transcript includes tips on exam techniques, such as the importance of clear diagrams and precise language in explanations.
The session concludes with a reminder of the value of practice and learning in physics, encouraging continued engagement with the subject.
Transcripts
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