Download Physics Laboratory #1: Simple Harmonic Motion

Physics Demonstration Lab#6.2: The Impulse-Momentum and WorkKinetic Energy Theorems on the Air Track
Name: ____________________________________Date: _________________________
EQUIPMENT
 PASCO Scientific Air Track and Accessories
 PASCO Scientific Force and Motion Sensors
 PASCO Scientific Science PowerLink Interface
 Personal Computer with PASCO DataStudio Software
PURPOSE
The purpose of this activity is to demonstrate how the Impulse-Momentum and WorkKinetic Energy Theorems can be utilized to analyze interactions between an object and
its surroundings.
THEORY
Impulse-Momentum Theorem: The change in momentum for an object is always equal to
the total impulse acting on the object during a given time interval. If the net force is
constant, the total impulse is equal to the product of the net force and the time interval
over which the net force acts:
Fnett  m(v f  vi )
If the net force varies over the time that the net force acts on the object, then the total
impulse may be found most effectively by determining area under the force-time graph.
Work-Kinetic Energy Theorem: The change in kinetic energy of an object is equal to the
net work done on the object as it moves over a given distance. If the net force is
constant, the net work is equal to the product of the net force and the distance over which
the net force acts:
1
Fnet d  m(V f2  Vi 2 )
2
If the net force varies over the distance that the net force acts on the object, then the net
work is equal to the area under a force-distance.
Useful Definitions:
 Impulse-Momentum Theorem:
o Impulse = Area under force-time graph (constant force => Impulse = force*time)
o Momentum = mass*velocity
o Total Impulse = Change in Momentum
o Units: N*sec = kg*m/sec
 Work-Kinetic Energy Theorem:
o Work = Area under force-distance graph (constant force => Work = force*distance)
o Kinetic Energy = ½ * mass * speed^2
o Net Work = Change in Kinetic Energy
o Units: N*m = kg*m^2/sec^2 = J (Joule)
PROCEDURE
Case#1 - Constant Net Force: Consider the apparatus illustrated below:
 Record the Mass of Air-Track Cart and the Angle of Track.
 Collect data as the Air-Track Cart travels down the incline using DataStudio
and compare those results with the enclosed graphs, which were collected
earlier for this case.
Motion Sensor
Air-Track Cart
Case#2 - Variable Net Force - Elastic Rebound: Consider the apparatus illustrated below:
 Record the Mass of Air-Track Cart / Magnet.
 Collect data as the Air-Track Cart travels along the air track and rebounds off
the magnet attached to the force sensor and compare those results with the
enclosed graphs, which were collected earlier for this case.
Motion Sensor
Air-Track Cart / Magnet
Magnet / Force Sensor
DATA
Case#1 - Constant Net Force:
Mass of Air-Track Cart:
_____ kg
Angle of Track:
_____ degrees
Graphs for earlier run: Position-Time, Velocity-Time, Acceleration-Time
Case#2 - Variable Net Force - Elastic Rebound:
Mass of Air-Track Cart:
_____ kg
Angle of Track:
_____ degrees
Graphs for earlier run: Position-Time, Velocity-Time, Acceleration-Time, ForceTime, and Force-Position
ANALYSIS/CONCLUSIONS:
Case#1 - Constant Net Force:
 Construct a Free-Body Diagram

Find the Net Force (component of gravity in direction of motion) algebraically

Add Force-Time and Force-Distance Graphs to your set of graphs

Calculate the change in momentum using mass and velocity data

Calculate the impulse algebraically

Calculate the impulse by calculating the area under the Force-Time Graph

Calculate the change in kinetic energy

Calculate the work algebraically

Calculate the work by calculating the area under the Force-Distance Graph

Complete the following statements by filling in the blank as appropriate:
The Impulse-Momentum Theorem _________ supported by this experiment.
The Work-Kinetic Energy Theorem ________ supported by this experiment.
Case#2 - Variable Net Force - Elastic Rebound:
 Construct Free-Body Diagrams for the time-frames indicated below:
cart moves at constant
velocity along the track
cart is being pushed backward
by the magnet attached to the
force sensor

Calculate the change in momentum during the entire rebound from the mass and
velocity data

Estimate the total impulse during the entire rebound by approximating the area
under the Force-Time Graph

Calculate the change in kinetic energy during the first half of the rebound (as the
cart is brought to rest by the magnetic force)

Estimate the net work done during the first half of the rebound (as the cart is
brought to rest by the magnetic force) by approximating the area under the ForceDistance Graph

Complete the following statements by filling in the blank as appropriate:
The Impulse-Momentum Theorem _________ supported by this experiment.
The Work-Kinetic Energy Theorem ________ supported by this experiment.
Case#1 - Constant Net Force:
Case#2 - Variable Net Force - Elastic Rebound: