Centripetal Force Lab Patrick yoha Period 6/7 Purpose of lab: To be able to determine the relationship between centripetal force, mass, velocity, and the radius of orbit for a body that is undergoing centripetal acceleration Background Information: Centripetal forces are forces that hold a revolving object in its circular path. It is center seeking, and necessary for circular motion. motion. Centrifugal forces are forces that are center fleeing, so they are the action/reaction pair to centripetal force. They are directed directed away from the center, and never act on revolving revolving objects. We learned a lot about these two forces and how they compliment each other. other. The euation for relating centripetal force, mass, radius of circle, and velocity is! "c # $m v %& / r !uipment and "et#$p: Tension "c
Tension
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This is the set up for the e(periment. The following is used for the project! )plastic tube )rubber stoppers of different si*e )nylon cord )different weighing hanging masses )stopwatch )meter stick )tape +asically, you set the apparatus up by fastening the nylon cord on the rubber stopper. With the other end of the nylon cord, you put it through the plastic tube, and secure a hanging weight on the end. The directions will specify the distance of the radius, and
also bits and pieces of the set up. nce the radius is known, set it up as told and place a piece of tape just below the bottom of the tube and above the hanging mass.
Procedural "ummary: -hysically what we did was swing the apparatus around in the air in a circular rotation, counting the number of rotations until it reached our given number of %. We changed the distance of the radius, the weight of the mass, and the si*e of the stopper to give us different results. The time it took for each variable was what we looked at, and helped us verify the relationship between different aspects for an occurrence undergoing centripetal acceleration. %ata:
Data
g n s i s y a r a M V g s n i u i y d r a a V R g r n e i p y p r o a t V S
Trial #
Hanging Mass (g)
Mass of Stopper (g)
Total Time (s)
Radius (m)
1
100
28.7
15.72
0.5
2
150
28.7
11.94
0.5
3
200
28.7
11.07
0.5
4
250
28.7
10.19
0.5
5
300
28.7
9.54
0.5
6
100
28.7
12.81
0.3
7
100
28.7
15.62
0.5
8
100
28.7
19.59
0.7
9
100
28.7
21.53
0.9
10
100
28.7
23.2
1
11
200
28.7
11.03
0.5
12
200
26.6
11.19
0.5
13
200
48.1
15.44
0.5
14
200
20.5
9.82
0.5
15
200
12.9
6.62
0.5
Calculations:
Calculations Trial #
Centripetal Force (N)
Period (s)
Circumfrence (m)
Velocity (ms)
1
0.981
0.786
3.14
0.199745547
2
1.4715
0.597
3.14
0.262981575
3
1.962
0.5535
3.14
0.283649503
4
2.4525
0.5095
3.14
0.30814524
5
2.943
0.477
3.14
0.329140461
6
0.981
0.6405
1.884
0.1470726
7
0.981
0.781
3.14
0.201024328
8
0.981
0.9795
4.396
0.224400204
9
0.981
1.0765
5.652
0.262517418
10
0.981
1.16
6.28
0.270689655
11
1.962
0.5515
3.14
0.28467815
12
1.962
0.5595
3.14
0.280607685
13
1.962
0.772
3.14
0.203367876
14
1.962
0.491
3.14
0.319755601
15
1.962
0.331
3.14
0.474320242
(ample of each type of calculation! Centripetal force (N))
Period (s) -
hanging mass 2
total time (s) # 24.5% s % %
( 0.12 # 2 ( 0.12 # .012 3 2 # .516 s
Circumference (m) – % ( 7.28 ( radius $m& # % ( 7.28 ( .4 m # 7.28 m Velocity (m/s) – circumference $m& ( total time $s& # 7.28 ( 24.5% # .200584485 m/s
&raphs:
Trial 1-5
Trial 6-10
Trial 11-15
rror 'nalysis: We had a few things that may have made our data the way it was. There were a few times that didn9t seem completely right. This may have been because when we were swinging the apparatus around: our counter may not have counted all the rotations correctly in the time space. ;epending if he missed one or counted an e(tra one, our time in seconds may have been a little too high or a little too low.
the force of gravity always pulling down, b ut they are cancelled out in this situation. The tension pulling the rubber stopper keeps the stopper in the circle. It9s a strong tension with us twirling it. %. =elative to the radius, the stopper would go away from it. 3ewton9s first law is the law of inertia. The object remains in its state of motion until an outside force is applied to it. The string breaking or us letting go is supported by 3ewton9s first law in us changing it: therefore making the stopper fly away from the radius. 3ewton9s %nd law is f#ma. The velocity of the stopper would be changed when this force is applied, sending it away from the radius. It maintains the same velocity until disturbed by us letting go or the nylon cord breaking. 7.
In conclusion, this was a very interesting lab. We found that changing the variables in our e(periment affected the results greatly, and gave us different times for everything. The centripetal force made the velocity go up, and the higher the velocity then the greater the radius of the circle. The velocity went down when the mass of the object was greater. We saw all of these things throughout our e(periment. We worked well together, and overcame the minimal problems we needed to. "iguring out how to get the calculations with >icrosoft (cel was a task, but we worked hard to achieve our goal. We now know the relationship between centripetal force, mass, velocity, and the radius of orbit for a body that is undergoing centripetal acceleration.
