AP Physics Laboratory #9.1: Center of Mass, Impulse, and
Conservation of Momentum
Name: ____________________________________ Date: ________________________
Lab Partners: ____________________________________________________________
EQUIPMENT
 PASCO Scientific Air Track and Accessories, Force Sensor, Motion Sensor, and
Power Link
 Personal Computer running PASCO Data-Studio Software
PURPOSE
The purpose of this laboratory is to collect and analyze data in an effort to support of a
variety of ideas covered in the Center of Mass, Impulse, and Momentum Unit of study.
THEORY
Center of Mass:
The x-coordinate for the center of mass for a set of discrete objects is given by the
equation that determines the x-coordinate for the balance point of the system:
1 n
xcom 
 mi x i
mtot i 1
n
mtot   mi
i 1
The y and z-coordinates are given by similar equations.
Impulse:
The impulse for a constant force is given by the product of the force and the time over
which the force is applied:
J  Ft
The impulse for a variable force is given by the area under the force-time graph:
t2
J   F (t )dt
t1
Change in Momentum:
The change in momentum for an object is given by the product of the object’s mass and
the change in velocity for the object:
p  m(v f  vi )
Impulse-Linear Momentum Theorem:
The Impulse-Linear Momentum Theorem states that the change in momentum for an
object under the action of a net force is equal to the area under the net force-time graph
(a.k.a. the net impulse of all external forces). In mathematical terms:
J  p
INDIVIDUAL EXPERIMENTS/DEMONSTRATIONS
1. CENTER OF MASS
a. Use the materials provided to create an object of uniform thickness that you
are confident you can mathematically determine the center of mass for, and
sketch it below.
b. Mathematically determine the location of the center of mass. Mark it’s
location on your object and on your sketch.
c. Experimentally determine the location of the center of mass by balancing your
object on a single support (like the eraser end of a pencil). Mark the location
on your object and on your sketch.
d. Hang your object from a spot on the edge and sketch a line that represents the
vertical direction that passes through the hanging location. Include this line
on your sketch. Now hang your object from a second spot on the edge and
sketch a new line that represents the vertical direction passing through the
second hanging location. Include this second line on your sketch. What do
you observe?
e. Comment regarding the level of agreement between your mathematical and
experimental analysis.
2. 1-D REBOUND
a. The apparatus used for this experiment is illustrated below. The PASCO
Motion and Force Sensors should be connected to the computer via the
PASCO PowerLink Interface. Set the sample rate at 50Hz for the force
sensor and 20Hz on the motion sensor. Display Position-Time, VelocityTime, and Force-Time (Pull Positive) on a single graph window. Tare the
force sensor before collecting data.
Motion Sensor
Air-Track Cart / Magnet
Magnet / Force Sensor
b. Collect data for the cart as it moves down the track (launch speed of
approximately 0.50 m/sec) and rebounds from the far end. Print and
include the graphs. Don’t forget to measure the mass of the cart!
c. Analyze the data to test the Impulse-Momentum Theorem, by using the
Velocity-Time graph to determine the change in momentum and the
Force-Time graph to determine the impulse.
3. 1-D HARMONIC OSCILLATION
a. The apparatus used for this experiment is illustrated below. The PASCO
Motion and Force Sensors should be connected to the computer via the
PASCO PowerLink Interface. Set the sample rate at 50Hz and display
Position-Time, Velocity-Time, and Force-Time (Pull Positive) on a single
graph window. Tare the force sensor when the mass is hanging at rest.
Force Sensor
Spring
1.0Kg
Motion Sensor
b. Collect data for the mass as it oscillates over a few periods. Print and
include the graphs.
c. Analyze the data to test the Impulse-Momentum Theorem as the mass
moves from it’s midpoint on the way up to it’s midpoint on the way down,
by using the Velocity-Time graph to determine the change in momentum
and the Force-Time graph to determine the impulse.
d. Determine the constants associated with the following functional forms of
position, velocity, acceleration, and net force.
x(t )  A sin( Bt  C )  D
v(t )  E cos( Bt  C )
a(t )   F sin( Bt  C )
FNET (t )  G sin( Bt  C )
e. Determine the impulse over the same time interval as c. by determining
the definite integral of the net force with respect to time over the
appropriate time interval. Comment regarding the level of agreement of
your answer with the answer to c.