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```Forces at Equilibrium
Fatima S. Al-Mubarak
ID# 201002225
Group members:
Fatima Al-Mubarak
Sara Al-Towaijri
Haifa Al-Humayyed
Miznah Al-Zamil
Section: 211
Submission date: 01-10-2012
PHYS 1411: Introductory Physics Lab
Lab Instructor: Nouf Al-Jalaud
Fall 2012-2013
1. Abstract (Objective)
The objective of this experiment is about understanding forces equilibrium by testing
it. It is about trying to reach the balanced point by changing angles that holds various
masses and forces. You are supposed to have 3 main forces, 1 fixed (M3) and 2
changeable (M1 and M2). And by changing masses and angels, specific mathematical
procedure and calculations will lead you to the purpose of the experiment which is
adding the results to be equal to the fixed force (M3).
2. Theory
The theory behind this experiment is mainly Newton’s second law. The mathematical
formulas used in calculations were:
1- (M1sinθ1+ M2sinθ2= M3), where M1sinθ1 is force number 1 multiplied by
the Sin of its angel, and M2sinθ1 force number 2 also multiplied by the Sin of
its angel. M3 refers to the fixed force, which in my experiment were 20.
2- Average Value: Sum of all trials\number of trials
3- Percentage Error: (|Approximate Value-Exact Value) \ |Exact Value|) x
100. Which approximate value refers to Average Value, and Exact Value
refers to M3 (20).
3. Method
The experiment was based on specific procedure. We used a force table assembly that
has 3 super pulley clamps attached to 3 mass hangers all tied up by a thread. First,
force number 3 had a fixed mass in all trials and located at 270° angle. Second, we
started changing the masses and moving their angles with every trial to reach
equilibrium, and then record calculated results using mathematical rule.
4. Data
M3= 20 = at 270°
Trials
1
2
3
4
M1
40
20
15
30
θ1
54°
23°
19°
45.5°
sinθ1
0.8
0.4
0.23
0.71
M1sinθ1
32.26
7.8
4.88
21.39
M2
25
25
20
20
θ2
200°
144°
136°
177°
sinθ2
-0.34
0.58
0.69
0.05
M2sinθ2
-8.55
14.69
13.89
1.04
M3
23.8
22.4
18.4
22.1
5. Data Analysis (Results Discussion)
We are required to change masses of the 2 changeable forces (M1 and M2) every trial
and then change angles until balancing. We record the mass, record its angle,
calculate Sin of the angel and then multiply it by the mass to find the wanted result.
After doing these calculations with the both forces, we add the two final results and it
should be equal or closely equal to the mass of the fixed force M3, according to the
mathematical rule (M1sinθ1+ M2sinθ2= M3). Another thing is finding the Average
Value of all trials by adding all final answers (23.8 + 22.4 + 18.4 + 22.1) and divide
2
them by the number of trials (4). In addition to Percentage Error, which tells you your
percentage of errors in your calculation results by using this formula (|Approximate
Value-Exact Value) \ |Exact Value|) x 100, my percentage error in the experiment
was 8%.
6. Conclusion
In brief, the experiment was basically about balancing forces to reach equilibrium. It
taught me how to balance forces by first, balancing different masses and changing
angels, and second, using specific studied formulas. It also taught me that I should
always be precise with numbers in any experiment that includes mathematical rules
and calculations, because any tiny numerical mistake can lead to wrong results.
3
```
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