Pasco Scientific ME-8950 User manual

AC
C
E
SSO
RY
RO
TATI
O
N
ALI
NER
TIA
ROTATIONAL INERTIA
ACCESSORY
Instruction Manual and
Experiment Guide for
the PASCO scientific
Model ME-8950
012-05293E
8/97
©1994 PASCO scientific $10.00
COMPLETE ROTATIONAL
SYSTEM
1

Complete Rotational System 012-05293E
2
Equipment
50g masses (2)
100g mass with 3
open hooks
center post
side post
plastic
indicator disk spring
ME-8952 Centripetal Force Accessory Equipment
The ME-8952 Centripetal Force Accessory
includes:
- center post that supports an indicator mecha-
nism which consists of a small pulley, a mov-
able spring holder, a movable indicator, a
spring, and a plastic indicator disk
- side post for hanging hooked mass
- mass (100 g) with 3 open hooks
- 2 additional 50 gram masses
- clamp-on pulley
- 1 spool of thread
300g square mass (2)
with thumbscrews and
square nuts
low-profile
thumbscrew
assemblies (2)
aluminum rotating
platform
cast iron "A" base
"E" rings (2, 1 extra)
rotating vertical shaft
with 10-hole pulley
accessory
mounting rod
ME-8951 Rotating Platform Equipment
The ME-8951 Rotating Platform Includes the
following:
- PASCO cast iron “A” base with rotating shaft
and pulley with 10 holes
- aluminum track
- two square masses (about 300 g) with thumb
screw and square nut
- two additional low-profile screws and square nuts
to act as stops for the square mass in the Conser-
vation of Angular Momentum experiment
- accessory mounting rod for mounting the 10-
spoke pulley or the optional Smart Pulley photo-
gate head
- accessory mounting rod for mounting PASCO
Photogate (ME-9498A, ME-9402B or later)
clamp-on
pulley
spool of thread
photogate
mounting rod
2

Complete Rotational System 012-05293E
4
Assembly
ME-8951 Rotating Platform
Assembling the Rotating Platform
➀Insert the cylindrical end of the shaft into the bear-
ings on the top-side of the A-shaped iron base. Se-
cure the shaft in place by inserting the "E" ring in
the slot at the bottom of the shaft. See Figure 1.
➁Mount the track to the shaft and tighten the thumb
screw against the flat side of the “D” on the shaft.
See Figure 1.
"A" base
rotating platform
"E" ring
vertical shaft
thumbscrew
flat of vertical shaft
Figure 1: Attaching the Vertical Shaft to the Base and Rotating Platform Assembly
3

012-05293E Complete Rotational System
5
010 123456789
20 111213141516171819212224 10
987654321 20
191817161514131211 24232221
010
123456789
20
111213141516171819212224
10
987654321
20
191817161514131211 24232221
Figure 2: Leveling the Base
rotating platform
(rotated 90˚ as shown)
rotating
platform
in the pulley. If the photogate head is powered by a
computer, you can tell when the photogate is
blocked by watching the LED indicator on the end
of the photogate. The photogate head should not be
rubbing against the pulley. When the head is in the
correct position, tighten the bottom screw to fix the
rod in place.
"A" base
adjust this foot
first
leveling
feet
300g square
mass
300g square
mass
then adjust this
foot
Installing the Optional Smart Pulley Photogate Head
The black plastic rod stand is designed to be used in
two ways:
• It can be used to mount a Smart Pulley photogate
head to the base in the correct position to use the
10 holes in the pulley on the rotating shaft to mea-
sure angular speed.
• It can be used to mount a Smart Pulley (with the pul-
ley and rod) to the base to run a string over the pulley.
To Use the Photogate Head Only:
➀To install, first mount the black rod to the base by
inserting the rod into either hole adjacent to the
center shaft on the base.
➁Mount the Smart Pulley photogate head horizon-
tally with the cord side down. Align the screw hole
in the photogate head with the screw hole in the flat
side of the black rod. Secure the photogate head
with the thumb screw. See Figure 3.
➂Loosen the thumb screw on the base to allow the
black rod to rotate. Orient the rod and photogate
head so the infrared beam passes through the holes
thumbscrew
"A" base
Smart Pulley
photogate head
(optional) nylon
thumbscrew
10-spoke
pulley on
vertical shaft accessory
mounting rod
Figure 3: Using the Accessory Mounting Rod With
the Smart Pulley
Leveling the Base
Some experiments (such as the Centripetal Force
experiments) require the apparatus to be extremely
level. If the track is not level, the uneven performance
will affect the results. To level the base, perform the
following steps:
➀Purposely make the apparatus unbalanced by at-
taching the 300 g square mass onto either end of the
aluminum track. Tighten the screw so the mass will
not slide. If the hooked mass is hanging from the
side post in the centripetal force accessory, place
the square mass on the same side.
➁Adjust the leveling screw on one of the legs of the
base until the end of the track with the square mass
is aligned over the leveling screw on the other leg
of the base. See Figure 2.
➂Rotate the track 90 degrees so it is parallel to one
side of the “A” and adjust the other leveling screw
until the track will stay in this position.
➃The track is now level and it should remain at rest
regardless of its orientation.
photogate
mount rod
4

Complete Rotational System 012-05293E
6
10-spoke
pulley on
vertical
shaft
nylon
thumbscrew
accessory
mounting rod
"A" base
photogate
mounting
rod
Smart Pulley
photogate head
(optional)
Smart Pulley
Figure 4: Using the Accessory Mounting Rod With the
Photogate Mounting Rod and/or Smart Pulley
To use the entire Smart Pulley with rod
or the Super Pulley with rod:
➀Insert the Smart Pulley rod into the hole in
the black rod and tighten the set screw
against the Smart Pulley rod. See Figure 4.
➁Rotate the black rod so the string from the
pulley on the center shaft is aligned with the
slot on the Smart Pulley.
➂Adjust the position of the base so the
string passing over the Smart Pulley will
clear the edge of the table.
To mount a PASCO Photogate on "A" base:
➀Mount PASCO Photogate on threaded end
of rod (rod height may be adjusted with
thumbscrew).
➁Slide non-threaded end of photogate mount
into hole in base, clamp in place with
thumbscrew.
spring bracket
spring
square nut
center post
pulley
indicator
bracket
thumbscrew
reference mark
(center of post)
Figure 5: Center Post Assembly
ME-8952 Centripetal Force Accessory
Center Post Assembly
Assemble the center post as shown in Figure 5:
➀Attach one end of the spring to the spring bracket
and connect the indicator disk to the other end of
the spring. Insert the spring bracket into the slot on
the center post and tighten the thumb screw.
➁Tie one end of a string (about 30 cm long) to the
bottom of the indicator disk and tie a loop in the
other end of the string.
➂Insert the indicator bracket into the slot on the cen-
ter post, placing it below the spring bracket.
Tighten the thumb screw.
➃Attach the pulley in the higher of the two holes on
the center bracket.
➄Insert the thumb screw at the bottom of the center
post and attach the square nut.
indicator
disk
photogate
mount rod
5

012-05293E Complete Rotational System
7
Figure 6: Side Post Assembly
holes for
thread
thumbscrew
square nut
100g mass
single length
of thread
(30cm long) side post
nylon thumbscrew
Side Post Assembly
Assemble the side post as shown in Figure 6:
➀Insert the thumb screw at the bottom of the side
post and attach the square nut.
➁Using a string about 30 cm long, tie the string
around the screw head on the top of the side post.
Then thread the other end of the string down
through one of the holes in the top of the side post
and then back up through the other hole. Do not
pull the string taut.
➂Loosen the screw on the top of the side post and
wrap the loose end of the string around the threads
of the screw and tighten the screw.
1234
5
0
1
2
3
4
5
Figure 7: Threading the Centripetal Force Accessory
100g mass
indicator
bracket
side post
center post
zero mark
of rule
rotating
platform
thread
reference mark
(center of post)
pulley
Threading the Centripetal Force
Accessory
➀Mount the center post in the T-slot
on the side of the track that has the
rule. Align the line on the center
post with the zero mark on the rule
and tighten the thumb screw to se-
cure it in place. Then mount the
side post on the same side of the
track. See Figure 7.
➁Hang the object from the string on
the side post and adjust the height
of the object so the string coming
from the center post will be level.
indicator
disk
6

012-05293E Complete Rotational System
19
Experiment 3: Centripetal Force
EQUIPMENT NEEDED
- Centripetal Force Accessory (ME-8952) - Rotating Platform (ME-8951)
- stopwatch - balance
- graph paper (2 sheets) - mass and hanger set
- string
Purpose
The purpose of this experiment is to study the effects of varying the mass of the object, the
radius of the circle, and the centripetal force on an object rotating in a circular path.
Theory
When an object of mass m, attached to a string of length r, is rotated in a horizontal circle, the
centripetal force on the mass is given by:
F=mv
2
r=mr
ω
2
where vis the tangential velocity and ω is the angular speed (v = r ω ). To measure the velocity,
the time for one rotation (the period, T) is measured. Then:
v=
2
π
r
T
and the centripetal force is given by:
F=4
π
2mr
T2
Setup
Level the "A" base and rotating platform as described in the ME-8951 assembly section
on page 5.
Procedure
Part I: Vary Radius (constant force and mass)
➀The centripetal force and the mass of the hanging object will be held constant for this part of the
experiment. Weigh the object and record its mass in Table 3.1. Hang the object from the side
post and connect the string from the spring to the object. The string must pass under the pulley
on the center post. See Figure 3.1.
7

Complete Rotational System 012-05293E
20
➁Attach the clamp-on pulley to the end of the track nearer to the hanging object. Attach a string to
the hanging object and hang a known mass over the clamp-on pulley. Record this mass in Table
3.1. This establishes the constant centripetal force.
➂Select a radius by aligning the line on the side post with any desired position on the measuring
tape. While pressing down on the side post to assure that it is vertical, tighten the thumb screw
on the side post to secure its position. Record this radius in Table 3.1.
➃The object on the side bracket must hang vertically: On the center post, adjust the spring bracket
vertically until the string from which the object hangs on the side post is aligned with the vertical
line on the side post.
➄Align the indicator bracket on the center post with the orange indicator.
➅Remove the mass that is hanging over the
pulley and remove the pulley.
➆Rotate the apparatus, increasing the speed
until the orange indicator is centered in the
indicator bracket on the center post. This
indicates that the string supporting the
hanging object is once again vertical and
thus the hanging object is at the desired
radius.
➇Maintaining this speed, use a stopwatch to
time ten revolutions. Divide the time by ten
and record the period in Table 3.1.
➈Move the side post to a new radius and
repeat the procedure. Do this for a total of
five radii.
Analysis
➀The weight of the mass hanging over the pulley is equal to the centripetal force applied by the
spring. Calculate this force by multiplying the mass hung over the pulley by “g” and record this
force at the top of Table 3.2.
Figure 3.1: Centripetal Force Apparatus
rotating
platform
hanging
mass
center post
assembly
side post
assembly
clamp-on
pulley
"A" base
string
Radius Period (T) T
2
Mass of the object =
Mass hanging over the pulley =
Slope from graph =
Table 3.1: Varying the Radius
8

012-05293E Complete Rotational System
21
➁Calculate the square of the period for each trial and record this in Table 3.1.
➂Plot the radius versus the square of the period. This will give a straight line since:
r=
F
4
π
2
mT
2
➃Draw the best-fit line through the data points and measure the slope of the line. Record the slope
in Table 3.1.
➄Calculate the centripetal force from the
slope and record in Table 3.2.
➅Calculate the percent difference between
the two values found for the centripetal
force and record in Table 3.2.
Part II: Vary Force (constant radius and mass)
The radius of rotation and the mass of the hanging object will be held constant for this part of the
experiment.
➀Weigh the object and record its mass in Table 3.3. Hang the object from the side post and
connect the string from the spring to the object. The string must pass under the pulley on the
center post.
➁Attach the clamp-on pulley to the end of the track nearer to the hanging object. Attach a string to
the hanging object and hang a known mass over the clamp-on pulley. Record this mass in Table
3.3. This determines the centripetal force.
➂Select a radius by aligning the line on the side post with any desired position on the measuring
tape. While pressing down on the side post to assure that it is vertical, tighten the thumb screw
on the side post to secure its position. Record this radius in Table 3.3.
➃The object on the side bracket must hang vertically: On the center post, adjust the spring bracket
vertically until the string from which the object hangs on the side post is aligned with the vertical
line on the side post.
➄Align the indicator bracket on the center post with the orange indicator.
➅Remove the mass that is hanging over the pulley and remove the pulley.
➆Rotate the apparatus, increasing the speed until the orange indicator is centered in the indicator
bracket on the center post. This indicates that the string supporting the hanging object is once
again vertical and thus the hanging object is at the desired radius.
➇Maintaining this speed, use a stopwatch to time ten revolutions. Divide the time by ten and
record the period in Table 3.3.
➈To vary the centripetal force, clamp the pulley to the track again and hang a different mass over
the pulley. Keep the radius constant and repeat the procedure from Step #4. Do this for a total of
five different forces.
Centripetal Force = mg
Centripetal Force From Slope
Percent Difference
Table 3.2: Results (varying raduis)
9

Complete Rotational System 012-05293E
22
Table 3.3: Varying the Centripetal Force
Analysis
➀The weight of the mass hanging over the pulley is equal to the centripetal force applied by the
spring. Calculate this force for each trial by multiplying the mass hung over the pulley by “g”
and record the results in Table 3.3.
➁Calculate the inverse of the square of the period for each trial and record this in Table 3.3.
➂Plot the centripetal force versus the inverse square of the period. This will give a straight line
since:
F=4
π
2mr
T2
➃Draw the best-fit line through the data points and measure the slope of the line. Record the slope
in Table 3.3.
➄Calculate the mass of the
object from the slope and
record in Table 3.4.
➅Calculate the percent
difference between the
two values found for the
mass of the object and record in Table 3.4.
Part III: Vary Mass (constant radius and force)
The centripetal force and the radius of rotation will be held constant for this part of the experiment.
➀Weigh the object with the additional side masses in place. Record its mass in Table 3.5. Hang the
object from the side post and connect the string from the spring to the object. The string must
pass under the pulley on the center post.
➁Attach the clamp-on pulley to the end of the track nearer to the hanging object. Attach a string to
the hanging object and hang a known mass over the clamp-on pulley. Record this mass in Table
3.5. This establishes the constant centripetal force.
➂Select a radius by aligning the line on the side post with any desired position on the measuring
tape. While pressing down on the side post to assure that it is vertical, tighten the thumb screw
on the side post to secure its position. Record this radius in Table 3.5.
Centripetal Force = mg Period (T) 1
T
2
Mass of the object =
Radius =
Slope from graph =
Mass Over Pulley
Mass of Object (from scale)
Mass of Object (from slope)
Percent Difference
Table 3.4: Results (varying the centripetal force)
10

012-05293E Complete Rotational System
23
➃The object on the side bracket must hang vertically: On the center post, adjust the spring bracket
vertically until the string from which the object hangs on the side post is aligned with the vertical
line on the side post.
➄Align the indicator bracket on the center post with the orange indicator.
➅Remove the mass that is hanging over the pulley and remove the pulley.
➆Rotate the apparatus, increasing the speed until the orange indicator is centered in the indicator
bracket on the center post. This indicates that the string supporting the hanging object is once
again vertical and thus the hanging object is at the desired radius.
➇Maintaining this speed, use a stopwatch to time ten revolutions. Divide the time by ten and
record the period in Table 3.5.
➈Vary the mass of the object by removing the side masses. Keep the radius constant and measure
the new period. Weigh the object again and record the mass and period in Table 3.5.
Analysis
➀The weight of the mass hanging over the pulley is equal to the centripetal force applied by the
spring. Calculate this force by multiplying the mass hung over the pulley by “g” and record the
result at the top of Table 3.5.
➁Calculate the centripetal force for each trial using:
F=4
π
2mr
T2
and record this in Table 3.5.
➂Calculate the percent difference between the calculated centripetal force for each trial and mg.
Record in Table 3.5.
Questions
➀When the radius is increased, does the period of rotation increase or decrease?
➁When the radius and the mass of the rotating object are held constant, does increasing the period
increase or decrease the centripetal force?
➂As the mass of the object is increased, does the centripetal force increase or decrease?
Calculated
Centripetal Force
Period (T)
Mass hanging over pulley =
Centripetal Force = mg =
Radius =
Mass of Object % Difference
Table 3.5: Varying the Mass of the Object
11