Centripetal Force Lab
Gage Ames
Em DeLarme and Zack Armagost
Physics - Period 2
Wednesday, March 4, 2009
Purpose
To be able to understand and verify the relationship centripetal force, mass,
velocity, and the radius of orbit for a body that is undergoing centripetal acceleration.
Background Information
An object moving in the same direction is not necessarily undergoing
acceleration. If the object changes speed while moving in the same direction there is
acceleration (or deceleration). On the other hand, if the object moves at a constant
speed in the same direction, there is no acceleration. This does not mean that constant
speed always indicates no acceleration, however. An object that moves at a constant
speed and changes direction is also experiencing acceleration even though its speed
never changes. Both the acceleration produced by changing speed and the
acceleration produced by changing direction require a net force. This force that is
produced in called the centripetal force and the acceleration that causes a change in
direction is called centripetal acceleration.
Centripetal force means “center seeking.” It is the force responsible for keeping
an object in circular motion. If there were no centripetal force the object would fly off at
a tangent because of Newton’s First Law. This is demonstrated by spinning an object
on a string. If the string were to break or be cut, the object would fly out of its circular
path at a tangent.
An equation can be used to represent the relationship between centripetal force,
mass, velocity, and the radius of the circle. This equation is:
Fc 
mv2
r
Equipment and Setup







Plastic tube
Nylon cord
Several rubber stoppers of different sizes
Hanging masses
Stopwatch
Meter stick
Tape
Nylon cord
Setup
Rubber stopper
Plastic Tube
Person
Tape
Hanging Mass
Procedural Summary
String a plastic tube on the nylon cord and place a rubber stopper on one end
and a hanging mass on the other end. Hold the plastic tube and spin the rubber stopper
above the head in a circular path. Use a stopwatch to time how long it takes to make 20
rotations. Change the rubber stopper mass, length of string above the rube (radius),
and mass of the hanging mass and repeat to see how these factors affect the results.
Varying
Stopper
Varying
Radius
Varying
Mass
Data
Trial #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Hanging
Mass (g)
100
150
200
250
300
100
100
100
100
100
200
200
200
200
200
Mass of
Stopper (g)
45.3
45.3
45.3
45.3
45.3
45.3
45.3
45.3
45.3
45.3
45.2
13.1
28.4
39.6
72.5
Total Time
(s)
18.72
15.31
14.5
12.87
11.25
17.16
17.69
18.65
22.94
23.78
14.39
9.04
10.34
11.35
15.53
Radius (m)
0.5
0.5
0.5
0.5
0.5
0.3
0.45
0.6
0.75
1
0.5
0.5
0.5
0.5
0.5
Calculations
Varying
Stopper
Varying
Radius
Varying Mass
Trial #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Centripetal
Force (N)
(100
g/1000)*9.81
m/s2 = 0.981
1.4715
1.962
2.4525
2.943
0.981
0.981
0.981
0.981
0.981
1.962
1.962
1.962
1.962
1.962
Period (s)
18.72 s/20 =
0.936
0.7655
0.725
0.6435
0.5625
0.858
0.8845
0.9325
1.147
1.189
0.7195
0.452
0.517
0.5675
0.7765
Circumference
(m)
Velocity
(m/s)
2πr =
2*3.14*0.5 m =
3.14
3.14
3.14
3.14
3.14
1.884
2.826
3.768
4.71
6.28
3.14
3.14
3.14
3.14
3.14
3.14 m/0.936
s=
3.354700855
4.101894187
4.331034483
4.87956488
5.582222222
2.195804196
3.195025438
4.04075067
4.106364429
5.281749369
4.364141765
6.946902655
6.073500967
5.533039648
4.04378622
Graphs
Error Analysis
Some error in this lab may have been caused by the tape moving on the string or
the tape not being placed at exactly the right spot to begin with. When we placed the
tape and when we spun it, the tape was not in the exact same place. This caused the
radius to be longer or shorter depending on if the tape was higher or lower than when it
was measured, which would change the time and period.
Another source of error is the stopwatch we used. Sometime it would not start or
stop correctly. Other times it would stop and start again when the button was only
pressed once. This means the timing of the 20 revolutions may not have been the most
accurate, which would change our period lengths as well.
Finally how we spun the stopper may not have been consistent. The path may
have been slightly different or may have been spun faster or slower than necessary.
This would change our periods.
Questions and Conclusions
Tension
Tension
1.
Force of Gravity
Based on these diagrams one can see that the
tension is what is actually causing centripetal force
to be placed on the stopper as it rotates in circular
motion. The mass remained stationary during the
trials. This is because the tension applied to it and
the force of gravity acting on it were equal. This
means the only force left is the tension and
centripetal force to keep the stopper rotating.
2. If the string were to break the stopper would fly in a direction tangent to the circle.
This means it would be a 90° angle relative to the radius at that point. The reason
for this is that when the string breaks centripetal force is no longer keeping the
stopper in circular motion. It will therefore follow its normal path because of
Newton’s first law. It didn’t go straight before because an external force was acting
on it, but now that the centripetal force is gone, it will stay in its normal motion path
until acted upon by another outside force. When the stopper is in circular motion it
has acceleration because its direction is constantly changing. When the string
breaks, however, the stopper will move at a constant velocity therefore producing
no acceleration. This also means there is an absence of force according to
Newton’s Second Law.
3. As centripetal force increased, the velocity increased.
4. As the radius of the circle increased, the velocity increased.
5. As the mass of the moving stopper increased, the velocity decreased.
6. The centripetal force would need to decrease. This is because the radius is in the
denominator and increasing the denomination with a constant numerator (mass and
velocity) causes the quotient (centripetal force) to decrease.
Conclusion
This was a very successful lab overall. The graphs, the trend lines, and the
slope of the trend lines really helped me to understand how changing the different
factors in the centripetal force formula affects the results. I was able to verify the
relationships in a statistical and visual way. While not always the case, most of the
time I was able to visually see how the velocity changed with each trial. This
certainly helped me understand the relationship and trends between the variables.
Our data was able to show a clear trend as well, so the error must have been
minimal. It seems like the correlations of the lines of best fits are close to 1 or -1 as
well, so this also shows our data had quite regular trends.
If I were to do this experiment again I would be sure to use a more
dependable stop watch. Time was wasted when we had to perform trials again due
to the stopwatch stopping and then randomly starting. Some students used timers
on the internet with their laptops, which was a good idea. I will certainly do this next
time.