General Physics I Lab: Newton’s 2nd Law
Newton’s 2nd Law Equipment
Capstone
Motion sensor
Meter stick
Force sensor
Bench clamp
Rod for force sensor
Weights with hooks
Red glider
Blue glider
Air track
Photogate/smart pulley
String for gliders
Photo gate
Large picket fence
Digital scale
Index cards
Small table clamp
Photogate Sensor
Definition: A digital sensor shaped in the form of a U.
Functionality: An infrared beam (peaking at 880 nm) is passed between the legs of the 'U'.
Output when unblocked: High
Output when blocked: Low; light on the sensor turns on.
Timing mechanism:
Starts timing with a 10 kHz clock when the beam is blocked, stops when unblocked.
Cycle repeatedly when beam is alternately blocked/unblocked.
Applications:
With accessories (e.g., picket fences, pulleys), can calculate position, speed, acceleration, rotation, etc.
Force Sensor
Definition: An analogue sensor measuring force in Newtons (N) using a strain gauge.
Operational Characteristics:
Equipped with a hook.
Pushed: Records positive force.
Pulled: Records negative force.
Maximum measurable force: ±50 N (with conversion: 1 N = 0.2248 lb).
Calibration:
Calibration button in Tools column available for calibration.
Tare button zeros out the force sensor; can zero with a mass on it, allowing cancellation of a given force (useful feature).
Photogate/Smart Pulley
Definition: A digital sensor combining a photogate sensor with a pulley having spokes.
Functionality:
As the pulley turns, the spoke blocks the infrared beam.
Configured to display position, linear speed, linear acceleration, etc.
Picket Fence
Definition: A clear plastic sheet with regularly-spaced opaque bands.
Functionality: When passed through a photogate, it alternately blocks and transmits the infrared beam.
Programming Requirement: Capstone must be programmed for the distance between the bands (from the beginning of one opaque band to the next).
Purpose
Objective: To verify Newton’s 2nd Law and some applications of this law.
Theory
Definitions:
Let extbf{F} be the force in Newtons (N)
Let m be the mass in kilograms (kg)
Let extbf{a} be the acceleration in m ext{·} s^{-2}
Newton’s 2nd Law: extbf{F} = m extbf{a}
Contextual Note:
This law is a vector equation, but this lab focuses on linear motion, so vector notation is omitted.
The law can apply to a complete system or any part of it; assumes a rigid body not rotating.
Force extbf{F} is the sum of all forces acting on the chosen body/system, termed net force or total force.
Gravitational Force
Definitions:
Let m be mass of an object near Earth’s surface.
Let M be the mass of Earth.
Let R be Earth's radius.
Let G be Newton’s gravitational constant.
Gravitational force extbf{F}G : extbf{F}G = rac{GmM}{R^2} = mg
Acceleration due to gravity g :
g = rac{GM}{R^2} = 9.81 ext{ m·s}^{-2}
Applications of Gravitational Force
Weight in Newtons is mass (kg) times g = 9.81 ext{ m·s}^{-2} .
In free fall, if the only force is extbf{F}_G , then:
mg = ma ext{ or } g = a.
Experiments
Using Force Sensor and Motion Sensor
Description: Measure net force ($ extbf{F}$) on a mass ($m$) and measure acceleration ($a$) using the sensors.
Expected Result: The measured acceleration should equal rac{ extbf{F}}{m} .
Programming Setup
Ensure motion and force sensors are plugged in; note the inputs used.
Start Capstone from desktop; access Hardware Setup in Tools column.
Program sensors:
For motion sensor: Click on the digital input, select Motion Sensor II.
For force sensor: Repeat above step.
Click the orange tack to reduce overlapping interfaces.
Calibrating Force Sensor
Suspend the force sensor from a rod.
Click Record in Capstone to start calibration.
Hang a 0.5 kg mass on the hook of the force sensor.
Press the tare button on the force sensor to zero out the reading.
Click Calibration in Capstone Tools.
Select Force and continue.
Choose Two Standards for two-point calibration.
Enter “0” in the Standard Value for the first calibration point, then click Set Current Value to Standard Value.
After calibrating the first point, add two 0.2 kg masses to the sensor.
Weight of two 0.2 kg masses for second point:
0.4 ext{ kg} imes 9.81 ext{ m/s}^2 = 3.92 ext{ N} (should enter as negative).Set Current Value to Standard Value for the second calibration point.
Click Finish in calibration process.
Stop recording in Capstone.
Remove added masses, leaving the 0.5 kg.
In Tools, delete recorded data—this ensures the force sensor reads zero with the mass at rest. Future acceleration output is relative only to changes thereafter.
Graph Setup
Create graphs for force, position, velocity, acceleration by dragging graph icons to display. Configure each graph to show separate measurements.
Ensure graphs reflect a clean setup to aid smooth data representation.
Data Collection
Motion sensor should be on the floor, positioned adequately to avoid obstruction.
Attach an index card parallel to the floor on the hanging mass to aid reflections.
Move the force sensor vertically and record data while moving slowly through 5 cycles above the motion sensor.
Analyze the data for smoothness and resonance in the graphs.
Make use of graph analysis tools available in Capstone to evaluate data clarity and overlay measurements.
Analysis Questions
Compare force graph with acceleration graph; check for shape duplication.
Detail motion at zero crossings for velocity, acceleration, and force.
Discuss how sensor distance affects the graphs; identify variable differences if repositioned.
Select non-zero data from acceleration, compare with force graph values; establish relationships.
Testing Newton’s Laws on a System
Description: Connect two masses via a string; one mass ($M1$) hangs vertically while the other ($M2$, a glider) rests on a horizontal track.
Application of Newton’s 2nd Law:
Tension in string = T, common acceleration = a.
Positive directions: down for $M1$ and towards pulley for $M2$.
For $M1$: M1g - T = M_1a
For $M2$: T = M2a
Eliminating T provides the acceleration equation:
a = rac{M1g}{M1 + M_2}.
Assumptions: Pulley is massless and frictionless for tension equality; alternate scenarios may differ results.
Setup and Programming
Position a clamp at track's end; insert photogate/smart pulley.
Restart Capstone; ensure correct sensor programming.
Configure Timer settings and graph display selections to capture relevant data points.
Use red glider and level the air track appropriately before attaching masses for analysis.
Data Collection for Masses
Record movements while ensuring track mechanisms do not interfere with sensor outputs.
Analyze resulting linear speed graphs; apply linear fits to obtain relevant slope information, which indicates system behavior under gravity.
Repeat additional runs with various hanging masses while recording each corresponding speed of glider.
Results Analysis
Compare experimental results with theoretical predictions; identify discrepancies.
Draw free body diagrams for both masses, analyzing forces at play.
Experiments with Acceleration of Gravity
Description
A picket fence is dropped through a photogate sensor; acceleration is measured and compared to gravitational acceleration (g).
Setup and Programming
Assess installation of photogate near bench's edge; configure Capstone for the connected sensor.
Ensure the flag spacing for the picket fence is accurate (0.05 m).
Data Collection
Cushion floor area beneath the photogate to prevent damage to the picket fence.
Hold the picket fence above the photogate sensor, initiating Recording before releasing.
Take several runs to gain statistical confidence in the collected data.
Analyze acceleration using linear fits to derive meaningful results from the graphs.
Analysis Questions
Compare collected acceleration data against g; consider potential error sources.
Discuss the effects of changing drop heights on acceleration/speed data.
Analyze effects of initial velocities on acceleration/speed graphs.
Evaluate how increased mass influences acceleration results.
Conclusion
Responsibility note: Return equipment to original condition after use; prepare workspace for subsequent users.