AP Physics 1 2016 Free Response Solutions

Dan Fullerton

7 May 201627:14

EducationalLearning

32 Likes 10 Comments

TLDRIn this video, Dan Fullerton tackles the 2016 AP Physics 1 exam's free response questions. He provides detailed explanations and step-by-step solutions for various physics problems, including a rolling wheel on a ramp, a bouncing ball experiment, a cart on a track with speed bumps, a circuit with resistors, and a rope forming standing waves. Throughout the video, Fullerton emphasizes the importance of understanding fundamental physics concepts and applying them to real-world scenarios.

Takeaways

📚 The video discusses the 2016 AP Physics 1 exam free response questions and attempts to solve them based on the information available before the release of the official scoring guide.
🚀 Question 1 involves a wooden wheel rolling down a ramp, focusing on the forces acting on the wheel, the cause of angular acceleration, and the effect of ramp angle and friction on the wheel's motion.
📊 For Question 1 Part B, the problem examines the relationship between the force of friction and the wheel's linear acceleration, using Newton's second law to solve for the acceleration.
🔧 Question 2 explores the concept of perfectly elastic collisions with a toy ball, proposing an experiment to test the hypothesis that collisions deviate from perfect elasticity at higher speeds.
🎥 The proposed experiment in Question 2 involves dropping the ball from various heights and using a video camera and tape measure to record and analyze the drop and rebound heights.
📈 Data from the ball collision experiment in Question 2 should be represented in a graph or table, with the graph expected to show a deviation from a slope of one at higher collision speeds, indicating a loss of mechanical energy.
🏎️ Question 3 presents a unique transfer problem involving a cart on a track with speed bumps, requiring the sketching of a velocity-time graph and analysis of the cart's motion between bumps 41 and 44.
📉 In Question 3, the graph of the cart's velocity is expected to resemble a sawtooth pattern, with the cart's speed increasing linearly until it hits a bump and then decreasing.
🔄 Question 4 is a circuit problem involving four identical resistors, requiring the determination of the potential difference across each resistor from greatest to least.
🔌 For Question 4, Ohm's law is applied to find the current through each resistor and the potential drop across them, with the current through resistor C increasing when resistor B is removed.
🧵 Question 5 discusses a uniform rope hanging vertically and forming standing waves, with the problem focusing on the relationship between tension, wavelength, and wave speed along the rope.

Q & A

What is the main topic of the video?
-The main topic of the video is the analysis and solution of the 2016 AP Physics 1 exam free response problems.
How does the speaker introduce the first problem involving the wooden wheel?
-The speaker introduces the first problem by describing a scenario where a wooden wheel of mass M rolls down a ramp with a certain angle to the horizontal, and challenges the viewers to create a Freebody diagram and analyze the forces involved.
What force causes a change in the angular velocity of the wheel in the first problem?
-The force that causes a change in the angular velocity of the wheel is the static frictional force, as it applies a net torque to the wheel.
How does the speaker approach the second problem involving the bouncing ball?
-The speaker suggests designing an experiment to test the student's hypothesis about the ball's collisions with a hard surface, which involves dropping the ball from various heights and measuring the rebound height, using a video camera and a tape measure for accurate data collection.
What is the expected graph representation of the data collected in the bouncing ball experiment?
-The expected graph representation is a plot of rebound kinetic energy versus incident kinetic energy, which should show a straight line with a slope of one for a perfectly elastic collision, according to the student's hypothesis.
What is the basic principle that appears to be violated in the high-speed collision of the bouncing ball experiment?
-The basic principle that appears to be violated is the conservation of mechanical energy, as the graph seems to show more energy in the system than when it started, which is not possible in a closed system.
How does the speaker describe the motion of the cart in the speed bump problem?
-The speaker describes the motion of the cart as a sawtooth pattern, where the cart's speed increases linearly between bumps, reaches a maximum, and then decreases when it hits the next bump, continuing this pattern until it reaches a maximum average speed.
What happens to the maximum speed of the cart when the distance between the bumps is increased, according to the speaker?
-When the distance between the bumps is increased, the maximum speed of the cart is greater because it has more time to accelerate between bumps, and it takes a larger force (from the bumps) to return the cart to its prior speed.
What is the speaker's evaluation of the student's equation for the cart's maximum speed in the speed bump problem?
-The speaker evaluates the student's equation by noting that the data is not consistent with the equation because the graph shows a y-intercept that is not zero, which the equation does not account for.
How does the speaker explain the increased current through resistor C when resistor B is removed?
-The speaker explains that when resistor B is removed, the current through resistor C increases because the total resistance in the circuit decreases, leading to an increase in the total current, and since the current through C is now part of the main circuit, it experiences a higher flow.
What is the speaker's reasoning for the higher tension at the top of the rope in the standing wave problem?
-The speaker reasons that the higher tension at the top of the rope is due to the need to support more weight from the rope below, which results in a greater force and thus higher tension at points with more rope hanging below them.

Outlines

00:00

📚 Physics Exam Analysis: Rolling Wheel Problem

The paragraph discusses the analysis of a physics problem involving a wooden wheel rolling down a ramp. The speaker, Dan Fullerton, begins by sketching a free body diagram to understand the forces acting on the wheel, such as gravity, normal force, and static friction. He then explains how static friction causes angular acceleration, affecting the wheel's motion. The problem is approached from both a force and energy perspective, concluding that the frictional force分配s the wheel's acceleration. The speaker also discusses how the problem could be solved using Newton's second law and the concept of mechanical energy conservation.

05:00

🎾 Bouncing Ball Experiment: Elastic Collision Hypothesis

This section of the script outlines an experiment to test the hypothesis that a toy ball's collisions with a hard surface are nearly perfectly elastic at low speeds but become less so as the speed increases. The speaker proposes using a video camera and a tape measure to measure drop and rebound heights of the ball from various starting points. The data collected would then be analyzed by plotting rebound kinetic energy against incident kinetic energy to determine the elasticity of the collisions. The speaker anticipates that the graph would show a deviation from a perfectly elastic collision at higher speeds, indicating a violation of the conservation of mechanical energy.

10:01

🚂 Velocity and Time Analysis of a Cart on a Bumpy Track

The speaker tackles a complex problem involving a cart on a long track with speed bumps. The cart's motion is analyzed between the 41st and 44th bumps, where it reaches a maximum average speed. The speaker sketches a sawtooth graph to represent the cart's velocity over time and explains the pattern of acceleration and deceleration at each bump. He then discusses how increasing the distance between bumps or the angle of the track would affect the cart's maximum speed, concluding that both changes would result in an increase in speed due to longer acceleration times and greater gravitational force, respectively.

15:10

🔌 Circuit Analysis: Resistors in Series and Parallel

The speaker explains a circuit problem involving four identical resistors arranged in a specific configuration. Using Ohm's law, he calculates the potential difference across each resistor, determining their order from greatest to least. He then discusses the effects of removing one of the resistors on the current flow and the potential difference across the remaining resistors. The speaker provides a detailed analysis of the changes in current and voltage upon the removal of a resistor, emphasizing the impact on the overall circuit.

20:12

🧵 Tension and Waves in a Hanging Rope

In this part, the speaker addresses a problem concerning the tension in a rope with standing waves formed by an oscillator. He explains why the tension at a point higher up on the rope (Point P) is greater than at a lower point (Point Q), attributing it to the additional weight of the rope that Point P must support. The speaker also discusses a hypothesis that increasing the tension in the rope would increase the speed of wave travel. He supports this hypothesis by explaining the relationship between wavelength, amplitude, and the speed of wave propagation, concluding that a higher tension at the top of the rope corresponds to a higher wave speed, consistent with the wave equation.

Mindmap

Keywords

💡Freebody Diagram

A freebody diagram is a graphical representation that shows all the forces acting on an object in isolation. In the video, it is used to analyze the forces acting on a wooden wheel rolling down a ramp, including gravity, normal force, and static friction. It helps to visualize and calculate the effects of these forces on the wheel's motion, particularly its acceleration down the ramp.

💡Angular Velocity

Angular velocity is a measure of the rate at which an object rotates or spins around a specific axis. In the context of the video, it is related to the wheel's rotation as it rolls down the ramp. The speaker discusses how the force of static friction causes a change in the wheel's angular velocity, which is essentially an angular acceleration, indicating the wheel's rotational speed is increasing as it moves down the ramp.

💡Static Friction

Static friction is the force that prevents an object from moving or sliding when it is in contact with another surface. In the video, static friction is described as the force that opposes the motion of the wheel on the ramp and causes angular acceleration. The speaker explains that the magnitude of the static friction force on the wheel is 40% of the force directed down the ramp, which is relevant for calculating the wheel's linear acceleration.

💡Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. In the video, the speaker calculates the linear acceleration of the wheel on the ramp using Newton's second law, taking into account the forces acting on the wheel, such as gravity and static friction. The resulting acceleration is found to be independent of the wheel's mass and is proportional to the sine of the ramp's angle.

💡Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, typically related to its height above a reference point. In the video, the speaker discusses an experiment involving a block of ice and a wheel on a ramp, where the gravitational potential energy at the top of the ramp is converted into kinetic energy at the bottom. The amount of kinetic energy depends on whether the object is a block or a wheel, as the wheel has both translational and rotational kinetic energy.

💡Kinetic Energy

Kinetic energy is the energy an object has due to its motion. It is directly proportional to the mass of the object and the square of its velocity. In the video, the speaker talks about the conversion of gravitational potential energy into kinetic energy as an object moves down a ramp. The kinetic energy can be either translational, as in the case of the block of ice, or a combination of translational and rotational, as in the case of the wheel.

💡Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the video, this principle is discussed in the context of the block of ice and the wheel on the ramp. The speaker explains that all the gravitational potential energy at the top of the ramp is converted into kinetic energy at the bottom, with the block having more translational kinetic energy due to the absence of friction.

💡Elastic Collision

An elastic collision is a type of collision where both momentum and kinetic energy are conserved. In the video, the speaker discusses a hypothesis that collisions between a ball and a hard surface are nearly elastic at low speeds but become less so as the speed increases. The concept is tested through an experiment that measures the ball's rebound height from various drop heights.

💡Mechanical Energy

Mechanical energy is the sum of the kinetic and potential energies in a system. It is conserved in the absence of non-conservative forces like friction. In the video, the speaker discusses a scenario where the graph of rebound kinetic energy versus incident kinetic energy shows a deviation from the expected straight line, suggesting a violation of mechanical energy conservation.

💡Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. In the video, Ohm's Law is used to calculate the current flowing through a series-parallel circuit of resistors and to determine the potential difference across each resistor.

💡Standing Waves

Standing waves are waves that appear to stand still, formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions. In the video, the speaker discusses a uniform rope hanging vertically and forming standing waves when set into oscillation by an oscillator. The concept is used to explain why increasing the tension in the rope would increase the speed at which waves travel along it.

💡Wave Equation

The wave equation is a fundamental equation in physics that describes how waves propagate through a medium. It relates the speed of a wave to its frequency and wavelength. In the video, the wave equation is used to support the hypothesis that increasing the tension in a rope affects the speed of wave travel along it.

Highlights

Analysis of the 2016 AP Physics 1 exam free response problems.

Creation of a Freebody diagram for a wooden wheel rolling down a ramp.

Explanation of how static friction causes angular acceleration in the rolling wheel.

Calculation of the wheel's linear acceleration using Newton's second law and the force of static friction.

Comparison between the speed of a block sliding down a ramp and a wheel rolling down the same ramp.

Design of an experiment to test the hypothesis that collisions of a ball with a hard surface are perfectly elastic at low speeds.

Use of a video camera and tape measure to measure drop and rebound heights in the ball experiment.

Representation of data in a graph or table to determine the validity of the students' hypothesis.

Discussion on the violation of a basic physics principle in high-speed collisions.

Sketching a graph of velocity as a function of time for a cart moving between speed bumps on an inclined track.

Explanation of how increasing the distance between speed bumps affects the cart's maximum speed.

Analysis of the effect of increasing the incline angle of the track on the cart's maximum speed.

Critique of a student's equation for the cart's maximum speed and its consistency with experimental data.

Analysis of a circuit problem involving four identical resistors and determination of potential difference across each.

Discussion on the change in current through a resistor when another resistor is removed from the circuit.

Investigation of the relationship between tension in a rope and the speed of wave travel along it.

Explanation of how the weight distribution in a hanging rope affects the tension at different points.

Transcripts

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