## Description

### Overview

PASCO’s Advanced Physics through Inquiry 1 helps you prepare your students for the rigors of the AP* Physics 1 lab. Each lab is presented in three ways, allowing you to decide what level of inquiry is appropriate:

1) Structured

2) Guided Inquiry

3) Student Designed

This lab manual covers the new College Board Learning Objectives with data analysis and assessment questions designed to prepare students for the AP Physics 1 exam.

Each lab includes a teachers resource section with College Board Correlations, pre-lab discussion and questions, procedural overview, tips, and sample data, assessment and synthesis questions. The manual includes both the printed version and a CD copy with teacher tips, a PDF of teacher version, and an editable Word student version.

Instruction videos guide students through use of lab equipment.

*AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.

### Experiments

## Advanced Physics through Inquiry 1

**15 Experiments –** click an experiment for more details.

## Atwood’s Machine

### Lab Summary:

Students use a photogate and pulley system to determine the mathematical relationship between the acceleration of an Atwood’s machine, the difference between its two masses, and the sum of those two masses.

### Theory:

How is the acceleration of the two masses of an Atwood’s machine affected by their difference in mass and by their total mass? Experimentally determine the mathematical relationship between the acceleration of an Atwood’s machine, the difference between its two masses, and the sum of those two masses.

### Method:

The Structured version of this lab activity is divided into two parts:

Part 1 – Students transfer masses from the heavier side of the Atwood’s machine to the lighter side to vary the mass difference m2 – m1 (and thus net force) while keeping the total mass m2 + m1 constant. In each trial they determine the acceleration from the slope of a plot of the speed versus time while the masses were moving freely. Plotting acceleration versus the mass difference for all Part 1 trials will result in a straight line, and from that students are expected to determine the proportional relationship.

Part 2 – Students remove equal masses from both sides of the Atwood’s machine to vary the total mass m2 + m1 while keeping the mass difference m2 − m1 (and thus net force) constant and determine the resulting acceleration as in Part 1. Plotting acceleration versus the inverse total mass (1/total mass) will result in a straight line, and from that students are expected to determine the inverse proportional relationship.

Students are then asked to combine the two discovered proportionalities into an equation relating the three variables, and to determine the value of the proportionality constant k, which should be found to be near the value of the free fall acceleration due to gravity g.

Finally, students are asked to derive the equation for the theoretical acceleration of an Atwood’s machine and compare it to their experimentally-derived expression.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Coefficients of Friction

### Lab Summary:

Students use a motion sensor and a force sensor to determine the static and kinetic friction coefficients between two contacting surfaces.

### Theory:

How can the coefficients of kinetic and static friction between two surfaces be determined? Experimentally determine the static and kinetic friction coefficients between two contacting surfaces.

### Method:

Students use a force sensor to measure the force applied to start an object in motion and drag it across a surface at a constant speed (constant speed is assured by monitoring the velocity of the object using a motion sensor). Assuming the object’s speed is constant (net force is zero while the object is stationary and when it is moving), students can assume that the force applied to the object to start it in motion and drag it across the surface is equal and opposite to the frictional force experienced by the object. Using their graphs of applied force versus time, students identify the magnitude of the force corresponding to the static fs and kinetic fk frictional forces and record values for each.

In each trial, mass is added to the object, increasing the normal force and thus increasing both frictional forces. Students plot frictional (applied) force versus normal force for both static and kinetic force values. Using the slope of each best fit line, students determine experimental values for the coefficient of static friction and kinetic friction.

Combining these two proportionalities, students experimentally derive the equation that summarizes Newton’s Second Law.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Conservation of Mechanical Energy

### Lab Summary:

Students use a photogate and dynamics system to explore how a cart’s kinetic energy, gravitational potential energy, and total mechanical energy changes as it rolls down an inclined track.

### Theory:

How do the potential and kinetic energies of an object in a closed system change as its motion changes due to a conservative force? Design an experiment to explore how a cart’s kinetic energy, gravitational potential energy, and total mechanical energy change as it rolls down an inclined track.

### Method:

In the Structured version of this lab activity, students release a cart from several different heights on an inclined track and measure the different velocities of the cart, using a photogate, as it passes through a fixed reference point near the bottom of the track.

Using their measurements of height, students calculate the cart’s initial gravitational potential energy at the point from which the cart was released in each trial. Using both the speed and height of the cart at the reference point, students calculate the kinetic and gravitational potential energy of the cart at the reference point for each trial. Assuming that the total mechanical energy of the cart when it was released is equal to the cart’s initial gravitational potential energy, students compare that value to the sum of the cart’s kinetic and gravitational potential energy at the reference point.

Student data should show that the total mechanical energy of the cart when it was released is equal to its total mechanical energy at the reference point. Students then use this equality to establish that the total mechanical energy of the cart system is conserved.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Conservation of Momentum

### Lab Summary:

Students use a motion sensor and a dynamics system to demonstrate that linear momentum and kinetic energy are conserved in an elastic collision, and linear momentum is conserved but kinetic energy is not conserved in an inelastic collision.

### Theory:

How is the total linear momentum and kinetic energy of a two-object system affected by a collision? Experimentally demonstrate that linear momentum and kinetic energy are conserved in an elastic collision, and that linear momentum is conserved but kinetic energy is not conserved in an inelastic collision.

### Method:

The Structured version of this lab activity is divided into two parts:

Part 1 – Elastic Collisions: Students gently push one cart into a stationary second cart, producing a perfectly elastic collision using the magnetic bumpers on the carts. The magnetic bumpers repel each other without the carts ever making contact. Students use a balance and two motion sensors to measure the mass of the carts and the velocity of each cart just before and just after the collision, and then use those values to calculate the total momentum and kinetic energy of the system before and after the collision. Students repeat this process two additional times, increasing the mass of the stationary cart each time. Student data should show that the momentum and kinetic energy of the two car system are the same before and after the elastic collision in each trial.

Part 2 – Inelastic Collisions: Students follow the same procedure as in Part 1, but use the Velcro® bumpers on the carts instead of the magnetic bumpers, producing an inelastic collision in which the two carts stick together. The mass of each cart is measured in each trial, along with each cart’s velocity just before and just after the collision. Using their measured values for mass and velocity, students calculate the total momentum and kinetic energy of the system before and after the collision in each trial. Student data should show that the total momentum of the system is the same before and after the inelastic collision in each trial, but the kinetic energy is not.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## DC Circuits

### Lab Summary:

Students use a voltage–current sensor and an AC/DC electronics laboratory to construct simple resistor circuits with resistors in series or in parallel, or both (with at most one parallel loop of resistors), to demonstrate the validity of Kirchhoff’s loop rule (conservation of energy), and Kirchhoff’s junction rule (conservation of charge).

### Theory:

Are the total charge and total energy in an electrical circuit conserved? Does the sum of the voltage drops across each circuit component equal zero (conservation of energy); does the sum of currents going into a circuit junction equal the sum of currents going out of the junction (conservation of charge)? Construct simple resistor circuits with resistors in series or in parallel, or both (with at most one parallel loop of resistors), to demonstrate the validity of Kirchhoff’s loop rule (conservation of energy), and Kirchhoff’s junction rule (conservation of charge).

### Method:

In the Structured version of this lab activity, students construct a series circuit and a parallel circuit, using one battery and three resistors, ranging in resistance from 4.7 Ω to 33 Ω, and measure the current going through each circuit and the voltage drop across each circuit. They then measure the voltage drop, or change in electrical potential difference, across each element in the series circuit, and the current through each element in the parallel circuit. Using these measurements, students determine the behavior of the current at the junctions, as well as the change in potential across the series components within the circuit.

Students analyze their data using Ohm’s Law and equivalent resistance, and examine their results for evidence that supports the conservation of electric charge and conservation of energy. Students are expected to demonstrate that Kirchhoff’s loop and junction rules are valid for the analysis of DC circuits in series and parallel configurations.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Expansion Bundle (PS-2833)

## Graphical Analysis: Motion

### Lab Summary:

Students use a motion sensor to measure the position and velocity of a cart on a track to determine the graphical relationship between position, velocity, and acceleration versus time graphs.

### Theory:

How are the graphs of position versus time, velocity versus time, and acceleration versus time of an object undergoing constant acceleration related? Experimentally determine the relationships between the graphs of position, velocity, and acceleration versus time for an object undergoing constant acceleration, both positive and negative.

### Method:

The Structured version of this lab activity is divided into three parts:

Part 1 – Students use a motion sensor to measure the position and velocity of a cart on a level track as they push the cart down the track with constant velocity.

Part 2 – Students use a motion sensor to measure the position and velocity of a cart on an inclined track as they release the cart, which travels down the track with constant positive acceleration.

Part 3 – Students use a motion sensor to measure the position and velocity of a cart on an inclined track as they push the cart up the track with constant negative acceleration.

Based on their data from all three parts, students establish a graphical relationship between the curves of position, velocity, and acceleration versus time graphs for a cart in motion. Students are then given the shape of one of the motion graphs and using this relationship, they predict the shape of the curves of the other two graphs.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Momentum and Impulse

### Lab Summary:

Students use a motion sensor, force sensor, and dynamics system to investigate the relationship between the change in momentum of a cart undergoing a collision and the impulse imparted to the cart to change its momentum, and then use their data to establish a measurement-based relationship between change in momentum and impulse.

### Theory:

How is the impulse imparted to an object in a collision related to the change in momentum of the object? Investigate the relationship between the change in momentum of a cart undergoing a collision and the impulse imparted to the cart to change its momentum. Establish a measurement-based relationship between the change in momentum and the impulse.

### Method:

Students measure the following: the force imparted to a cart as it lightly collides with a spring bumper, the time interval during which the force is imparted, and the velocity of the cart before, during, and after the collision. The mass and the velocity of the cart just before and just after the collision are used to calculate the change in momentum of the cart as a result of the collision.

Students determine the average force and the time interval associated with the same collision using force versus time graphs and the statistical tools on their data collection system. The average force and the time interval are then used to calculate the impulse associated with the collision, and students compare their calculated impulse to their calculated change in momentum.

Students repeat this process 4 times and ascertain that the impulse associated with the collision of an object is equal to the change in momentum of the object.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Newton’s Second Law

### Lab Summary:

Students use a motion sensor to determine the relationship between a system’s mass, acceleration, and the net force being applied to the system.

### Theory:

What factors affect the acceleration of an object or system? Experimentally determine the relationship between an object’s or system’s mass, acceleration, and the net force being applied to the object or system.

### Method:

The Structured version of this activity is divided into two parts. In both parts, students use a dynamics track and cart and set up the system so a mass hangs over a pulley at the end of the level track, accelerating the cart as the mass falls to the floor.

Using a motion sensor mounted at the end of the track opposite the pulley, students measure the cart’s velocity as it accelerates, and then use the slope of the velocity versus time graph to determine the cart’s acceleration.

Part 1 – Students keep the amount of hanging mass constant (constant net force) while varying the mass added to the top of the cart (varying system mass), and observe how this affects the acceleration of the system. Student data will show a linear relationship between acceleration and 1/mass.

Part 2 – Students keep the system mass constant but change the net force acting on the system by moving mass from the top of the cart to the mass hanger, and observe how this change affects the acceleration of the system. Student data will show that the acceleration of the cart is proportional to the net force acting on the cart.

Combining these two proportionalities, students experimentally derive the equation that summarizes Newton’s Second Law.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Periodic Motion: Mass and Spring

### Lab Summary:

Students use a motion sensor to determine the physical properties of a hanging mass and spring system that affect its period of oscillation, and then use their data to support a mathematical model relating period, mass, and spring constant.

### Theory:

What variables affect the period of oscillation of a mass and spring system? Experimentally determine the physical properties of a hanging mass and spring system that affect its period of oscillation.

### Method:

The Structured version of this lab activity is divided into four parts:

Part 1 – Students assemble a vertical mass and spring system and then displace the mass vertically to set the system into oscillatory motion. Students measure the period Ts of their system as it oscillates, while increasing the initial vertical displacement of the mass in each trial. They measure the time for ten cycles of motion in each trial and use this time to determine the average period of the system. Student data will show that the average period in each trial is identical, or nearly identical, prompting students to recognize that the period of a mass and spring system is unaffected by changes in initial vertical displacement.

Part 2 – Using the same setup as in Part 1, students measure the average period of two mass and spring systems with identical spring constant and hanging mass, but different length. Student data will show that the average period for each system is identical, or nearly identical, prompting students to recognize that the period of a mass and spring system is unaffected by the length of the system.

Part 3 – Using the same setup as in Part 1, students measure the average period of three mass and spring systems with identical length and mass, but different spring constant. Students calculate 1/√spring constant for each system, and then plot a graph of period versus 1/√spring constant. The plot of period versus 1/√spring constant will show a linear (proportional) relationship. Students are expected to recognize that the period of a mass and spring system is proportional to the inverse square root of the spring constant.

Part 4 – Using the same setup as in Part 1, students measure the average period of a mass and spring system while increasing the amount of hanging mass in each trial. Students calculate √mass for each trial, and plot a graph of period versus √mass. The plot of period versus √mass will show a linear (proportional) relationship. Students are expected to recognize that the period of a mass and spring system is proportional to the square root of the hanging mass value.

Combining the results of all four parts of the lab activity, students use their data to support the actual mathematical relationship between period, mass, and spring constant for a mass and spring system.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Resonance and Standing Waves

### Lab Summary:

Students use a resonance air column, tuning forks, and the principles of resonance and standing waves for a pipe with one closed end to experimentally determine a value for the speed of sound in air.

### Theory:

How can standing waves be used to determine the speed of sound in air? Use sound waves traveling into a tube with one closed end and the principles of resonance and standing waves to experimentally determine the speed of sound in air.

### Method:

In the Structured version of this lab activity, students use a tube with one closed end and adjustable length to identify the length of tube required to establish the first harmonic (one standing wave with one-quarter wavelength inside the tube) for 5 different sound wave frequencies. Students then plot a graph of sound wave frequency versus inverse tube length. This graph displays a linear relationship to which students apply a line of best fit whose slope is equal to one-fourth the speed of sound in air. Using the slope, students calculate the speed of sound in air.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Expansion Bundle (PS-2833)

## Rotational Dynamics

### Lab Summary:

Students use a rotary motion sensor to determine the mathematical relationship between torque, rotational inertia, and angular acceleration of a rotating object.

### Theory:

How do net torque and rotational inertia affect the angular acceleration of a rotating object? Experimentally determine the mathematical relationship between net torque, rotational inertia, and angular acceleration of a rotating object.

### Method:

The Structured version of this lab activity is divided into two parts:

Part 1 – Students use hanging masses to apply torque to a rotating arm, oriented horizontally (see figure below). In each Part 1 trial, students keep the rotational inertia of the arm constant and measure its angular acceleration while increasing the amount of applied torque by adding more hanging mass. A plot of angular acceleration versus net torque will show a straight line, and from that, students are expected to recognize the proportional relationship.

Part 2 – Students use a fixed hanging mass to apply a constant non-zero net torque to the same rotating arm used in Part 1 while measuring the angular acceleration of the arm; however, in each Part 2 trial they keep the applied torque (amount of hanging mass) constant and vary the rotational inertia of the rotating arm by adjusting the position of two masses fixed to the rotating arm. Rotational inertia is increased as the masses are positioned farther from the axis of rotation. Students calculate the rotational inertia of the arm in each trial and then calculate the inverse rotational inertia (1/rotational inertia). A plot of angular acceleration versus the inverse of rotational inertia will show a straight line, and from that, students are expected to recognize the proportional relationship.

Students are then expected to combine the relationships outlined in each part into one mathematical expression relating the three variables.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

and

Advanced Physics 1 Expansion Bundle (PS-2833)

## Rotational Statics

### Lab Summary:

Students use a force sensor and tension protractor to demonstrate that the sum of the forces acting on an object in static translational equilibrium is equal to zero, and the sum of the torques acting on an object in static rotational equilibrium is equal to zero.

### Theory:

What must the net force and net torque on an object be if the object is in static equilibrium (translational and rotational)? Experimentally demonstrate that the sum of the forces acting on an object in static translational equilibrium is equal to zero, and the sum of the torques acting on an object in static rotational equilibrium is equal to zero.

### Method:

The Structured version of this lab activity is divided into two parts:

Part 1 – Students suspend a 500-g mass from two lengths of thread and use two PASCO Tension Protractors to measure the tension and angle applied to the mass by each thread. Students then calculate the component forces acting on the mass as it hangs motionlessly, and sum each set of component forces. This process is repeated for two additional trials; each trial with a different thread length configuration. Student data for each trial will demonstrate that the sums of the component forces acting on the mass in static equilibrium are equal to zero (or nearly zero) for both the x- and y-directions.

Part 2 – Students balance a meter stick on a fulcrum (directly under its center), and then place a 100-g mass at different distances from the fulcrum (pivot point) while applying a force, using a force sensor, to the meter stick on the opposite side of the pivot. When the applied force is enough to balance the meter stick and mass (static equilibrium), students record the force applied by the force sensor, the distance from the pivot to the force sensor, and the distance from the pivot to the mass. Students then calculate the torques applied to the meter stick by the mass and the force sensor and demonstrate that when the meter stick is in static equilibrium, the sum of the torques is zero, regardless of where the mass and force sensor are positioned.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Simple Pendulum

### Lab Summary:

Students use a photogate and pendulum to determine the physical properties of a simple pendulum that affect its period, and then use their data to support a mathematical model relating period to pendulum arm length.

### Theory:

What variables affect the period of a pendulum? Determine the physical properties of a simple pendulum that affect its period.

### Method:

The Structured version of this lab activity is divided into three parts:

Part 1 – Students build a simple pendulum using a pendulum bob and thread and then measure the period T

_{p} of their pendulum while increasing the horizontal displacement of the pendulum bob in each trial. Ten periods are measured in each trial and averaged. A plot of the average period versus displacement will show a straight horizontal line. From that, students are expected to recognize that the period is constant regardless of the magnitude of initial displacement of the pendulum.

Part 2 – Using the same setup as in Part 1, students measure the period of their pendulum while increasing the mass of the pendulum bob in each trial. Ten periods are measured in each trial and averaged. A plot of the average period versus mass will show a straight horizontal line. From that, students are expected to recognize that period is constant regardless of the magnitude of the pendulum bob mass.

Part 3 – Using the same setup as in Part 1, students measure the period of their pendulum while increasing the pendulum arm length (length of thread used). Ten periods are measured in each trial and averaged. A plot of the average period versus pendulum arm length will show a curved, or non-proportional, relationship establishing that the period is affected by the length of the pendulum arm. Students then use their data to calculate √Pendulum arm length. A plot of the average period versus √Pendulum arm length will show a linear (proportional) relationship. Students are expected to recognize that the period is proportional to the square root of the pendulum arm length and use their data to support the actual mathematical relationship between period and pendulum arm length.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

## Two Dimensional Motion: Projectiles

### Lab Summary:

Students use a photogate and mini launcher to measure the variables that affect the two-dimensional motion of a projectile launched horizontally, and then use those variables to accurately predict and test the projectile’s horizontal range.

### Theory:

What is the range of a projectile launched horizontally? Develop a plan to measure the variables that affect the two-dimensional motion of a projectile launched horizontally, and then use those variables to accurately predict and test the projectile’s horizontal range.

### Method:

Students assemble and mount a projectile launcher to their lab table and then make measurements of the variables (initial height and initial velocity) affecting the range of the projectile as it is launched horizontally. Students use their measurements to calculate a predicted value for the range of their projectile, and then they test their prediction. Students qualitatively analyze the accuracy and precision of their launcher based on the predicted range and the distribution of their actual range values.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)

and

Advanced Physics 1 Expansion Bundle (PS-2833)

## Work and Kinetic Energy

### Lab Summary:

Students use a photogate and dynamics system to investigate the relationship between the change in kinetic energy of an object experiencing a non zero net conservative force and the work done by that net force on the object, and then use their data to establish a measurement-based relationship between work and kinetic energy.

### Theory:

How is the work done on an object by a non-zero net conservative force related to the change in that object’s kinetic energy? Investigate the relationship between the change in kinetic energy of an object experiencing a non-zero net conservative force, and the work done by that net force on the object. Establish a measurement-based relationship between work and kinetic energy.

### Method:

Students use a cart and track system to show that the change in kinetic energy of a cart as it rolls down an inclined track is equal to the work done on the cart by gravity to displace it down the track.

To show this, students release a cart on an inclined track from various positions and measure its speed and displacement at the bottom of the track. Assuming that the initial speed of the cart just as it was released was zero, students use their cart mass m and speed v measurements to calculate the change in kinetic energy (ΔK = 1/2mΔv2) of the cart as it traveled from the point where it was released to the bottom of the track in each trial. Students then use the displacement d, the angle θ between the track and the downward force from gravity, and the force F due to gravity (F = mg) acting on the cart to calculate the amount of work W done by gravity to displace it (W = Fdcos θ).

Students’ calculated values for the work done by gravity on the cart and the cart’s change in kinetic energy should be nearly equal in each trial. From this, students are expected to ascertain that the work done on the cart by gravity to displace it down the track is equal to the change in the cart’s kinetic energy after being displaced.

### Your Bundle Options:

**Option 1:**

Advanced Physics 1 Starter Bundle (PS-2815)