AP Physics C
Projectile Motion Lab
Objective: The lab aims to calculate kinematic quantities of a projectile in motion, focusing on finding an expression for the range, independent of time.
Procedure: It involves collecting data without air resistance, graphing and linearizing results, and analyzing slopes
Findings: The experiment concluded that the distance traveled by a projectile is quadratically related to its initial velocity squared, with the relationship expressed as Δx=0.0349v2
Calculus Grapher
Objective: The lab aims to help students understand the motion of objects with nonuniform acceleration by exploring the relationships between position, velocity, and acceleration, and their corresponding calculus concepts such as integrals and derivatives.
Procedure: Students use the PhET Calculus Grapher tool to manipulate functions and observe changes in their derivatives. They analyze extrema, rate of change, and concavity to understand how these features relate to the function’s derivatives.
Results and Conclusions: Key observations include the correlation between the extrema of a function and constant values in its derivative, the representation of instantaneous rate of change in derivatives, and the impact of concavity on the sign of the second derivative.
Post Lab Questions: The lab includes questions that reinforce the physical interpretation of calculus concepts, such as relating position to velocity and acceleration, and understanding the derivatives of linear and quadratic functions in terms of motion.
Atwood’s Machine
The Atwood’s machine lab conducted by Junyu Xu and Alexander Fernandez at Yuxiang Primary School in Beijing focused on calculating the acceleration of a system under a net constant force. They derived Newton’s second law for the system and compared theoretical predictions with empirical data. The lab found that for equal masses (M=m), the acceleration is zero, while for a much greater mass (M>>m), the acceleration approaches the acceleration due to gravity (g) as M increases. The experiment also considered factors like air resistance and virtual mass that could affect the measured acceleration, suggesting ways to mitigate these errors. Lastly, the lab proposed a method to graphically estimate the value of g using the provided data, but the specific graphing approach was refused in the document.
Terminal Velocity
The lab focused on Air Resistance and Terminal Velocity using coffee filters to study the effects of air resistance on falling objects. The experiment involved dropping stacks of coffee filters and measuring their terminal velocity, which increased with the number of filters due to their linear mass relationship. Two key formulas derived were for terminal velocity under linear drag force ( v = \frac{mg}{b} ) and quadratic drag force ( v = \sqrt{\frac{mg}{k}} ). The results showed a power relationship between terminal velocity and the number of filters, with the data fitting well to the model ( v = 0.7631n^{0.5862} ) and ( v = 0.1277n^{0.5} + 0.7772 ), indicating significant air resistance effects in the lab setting. Errors from filter flutter could be minimized in a controlled environment with fewer air currents.
Impulse-Momentum Lab
Objective: The lab aimed to relate impulse to the change in velocity of an object by calculating the change in momentum, using a function of net force over time.
Key Experiment: Using a simulation, data was collected for force and time during several trials to measure the velocity of an astronaut character named Wally, while keeping his mass constant.
Findings: The final velocity was found to be linearly related to the force, confirming the initial expectations based on the impulse-momentum relationship.
Real-world Application: The experiment assumed no mass loss for Wally, which is not true in reality, as expelling gas from the fire extinguisher would decrease his mass and affect the force and momentum.
Newton’s Laws: The results demonstrated the relevance of Newton’s second law (F=ma) in relating velocity to force and mass, and the third law in understanding the forces acting on the astronaut4
Ballistic Pendulum
The ballistic pendulum lab is an AP Physics C – Mechanics experiment designed to study the conservation of energy and momentum. Students observe a bullet/marble fired into a block suspended by rods, which then swings like a pendulum. The goal is to determine the relationship between the initial velocity of the bullet and the pendulum’s height, verified through graphing and theoretical calculations. Results indicate a direct relationship between the bullet’s velocity and the maximum height achieved by the block. The lab also explores the fraction of kinetic energy remaining after the collision, enhancing understanding of inelastic collisions.
Inelasticity
Objective: The lab aimed to quantify the inelasticity of collisions using tennis and ping pong balls.
Methodology: Experiments involved dropping balls from a constant height and measuring their bounce heights to calculate elasticity. Findings: It was observed that the coefficient of elasticity decreases with increased drop height, indicating more energy loss in higher drops.
Challenges: Sources of error included difficulty in measuring the maximum height post-bounce and potential air resistance effects.
Rolling Motion
The rolling motion inquiry lab focuses on the kinetic energy of rolling objects, exploring the relationship between translational and rotational kinetic energy. Here are the key findings: Kinetic Energy Types: Objects exhibit translational kinetic energy (Kt=21mv2 ) when moving as a whole, and rotational kinetic energy (Kr=21Iω2 ) when rotating. Energy Conversion: Approximately 75% of gravitational potential energy converts to translational KE, while around 27.2% converts to rotational KE, with variations depending on mass and angle. KE Ratios: The ratio of rotational to translational KE is closest to 1/3, changing with different masses and angles. Cylindrical Disk vs. Ball: A cylindrical disk would have more translational KE and less rotational KE compared to a ball due to its lower tendency to rotate. This lab demonstrates the dual nature of kinetic energy in rolling motions and how object shape affects energy distribution.
Restoring Forces/Oscillations and DiffEqs
Objective: The lab aimed to derive a differential equation for a spring-mass system under Newton’s Second Law, connecting oscillations with the laws of motion.
Methodology: Students used a mass-spring system to experimentally determine the spring constant and measure the period of oscillation using a motion sensor and PASCO interface.
Results: The lab found that the slope of the acceleration vs. position graph should be the negative spring constant divided by mass, but observed values varied and were not directly related to these quantities.
Conclusion: The discrepancies in data were attributed to potential errors in data collection and processing, such as the mass oscillating out of the sensor’s range and inexperience with the Capstone software.
Period Observation: It was noted that the period of oscillation remained consistent despite changes in amplitude, supporting the theory that period does not depend on amplitude in an ideal spring system.
E/M!
Gauss’s Law Lab
Gauss’ Law Fundamentals: The lab focuses on understanding Gauss’ Law and its application in calculating electrical flux through a 3D surface based on the enclosed charge.
Flux and Charge Relationship: Through interactive simulations, it demonstrates that flux is directly proportional to the amount of charge within an imaginary surface.
Charge Distribution Impact: The lab illustrates how different charge distributions, including point charges and combinations of positive and negative charges, affect the flux.
Key Conclusion: A pivotal conclusion is that when no charge is present within the surface, the flux is zero, highlighting the dependency of flux on the presence of charge sources.
Equipotentials and Electric Fields
Electric Field Direction: The lab demonstrates that the electric field is perpendicular to equipotential curves, with the field direction also being perpendicular relative to the surfaces.
Equipotential Magnitude: It is shown that the magnitude of the electric field is not constant across an equipotential, indicating that the potential varies at different points.
Charge Enclosure: The investigation reveals that a closed equipotential surface can only enclose charges of one sign, as opposite charges would have different directions of acceleration.
Positive Charge Acceleration: Positive charges are found to accelerate towards negative potentials, as like charges repel and unlike charges attract.
Millikan Oil Drop
The lab involves:
Determining Mass: Calculating the mass of oil droplets experiencing quadratic drag.
Electric Field Application: Using a uniform electric field to adjust droplet velocity until they are at rest, indicating equilibrium.
Charge Calculation: Analyzing the net charges of the droplets and observing trends in mass, charge, and the charge-to-mass ratio.
The findings suggest that as the applied voltage increases, so do the velocity, mass, and charge of the droplets, which aligns with the expected outcomes of the experiment. Possible sources of error include the influence of other droplets’ electric fields and the absence of air resistance in the simulation.
Capacitors
Objective: The lab aimed to explore the characteristics of capacitance in parallel plate systems, focusing on the relationships between voltage, charge, capacitance, and potential energy.
Key Findings: It was found that capacitance has an inverse relationship with plate separation and a direct relationship with plate area. Additionally, capacitance and stored energy were observed to be directly proportional.
Observations: When charging the plates and connecting them to a light bulb, both charge and potential difference decreased linearly.
Real-world Relevance: The lab also discussed the practicality of capacitors in real-world scenarios, such as in computers, phones, and cars, where they temporarily store energy.
Circuits/DC Circuits inclass
Objective: The lab aimed to understand the equivalent resistance in circuits by measuring voltage and current across resistors in series and parallel configurations.
Key Findings: It was observed that current remains constant through series resistors, while in parallel, the currents approximately add up to the total from the battery.
Errors and Variations: Possible errors included measurement inaccuracies and equipment quality, with a significant 89.67% percent difference in series circuit voltage and a 3.98% difference in parallel circuit current from theoretical values.
Resistivity Factors: The lab also discussed how temperature affects resistivity, which could contribute to experimental errors.
RC CIRCUITS
The RC Circuits lab focused on analyzing the impact of equivalent resistance and electromotive force (emf) voltage on the time constant of an RC circuit, which determines the charging and discharging times of a capacitor. Students conducted experiments to compare theoretical and experimental time constants, using a voltmeter and Capstone software to record voltage over time and apply a natural exponential trendline for calculations. The results showed that a larger capacitance led to longer charge/discharge times, with experimental time constants being consistently higher than theoretical values, indicating potential sources of error such as the internal resistance of the voltmeter. To improve accuracy, the lab suggests using more advanced equipment or accounting for the voltmeter’s internal resistance in calculations.
Ampere’s Law
Objective: The lab aimed to derive the magnetic field’s magnitude for certain current-carrying wires and an ideal solenoid using Ampere’s Law.
Key Discoveries: It was found that magnetic flux is non-zero only when the loop encloses a current, and the magnetic field strength depends on the current’s strength.
Ampere’s Law: The law states that the magnetic flux through a 2-D surface depends on the current enclosed by the surface and its perimeter.
Solenoid Field: The lab concluded that a solenoid produces a uniform magnetic field when approximated as a series of identical current loops stacked closely together. These findings help understand the relationship between current and magnetic fields in symmetrical configurations.
Faraday/Lenz’s law
Electromagnetic Induction: The lab demonstrates that a changing magnetic field induces an electric current in a conductive loop, confirming Faraday’s Law.
Lenz’s Law: It also shows that the induced current’s direction is such that it opposes the change in magnetic flux, illustrating Lenz’s Law.
Observations: Movement of a magnet near or inside the loop causes light to be generated, signifying the presence of electricity. The direction of current changes with the polarity of the magnet.
Applications: Understanding these principles is essential for technologies like generators, transformers, and magnetic levitation trains.