Download - Physics Force Table Lab Report
Mozaffari
Armeen Mozaffari
Honors Physics
Mr. Bostian
29 October 2013
6 November 2013
Finding the Equilibrant using Trigonometry
Abstract: For this experiment, we were trying to prove that trigonometry could be used in place
of a force table to find the equilibrant. The trigonometry way includes making two right triangles
with the given angles and the given forces. Then, we use trigonometry to figure out the massesx
and the massesy. Then, you add the massesx together and the massesy together and make a new
triangle with the sums. After that, you figure out the hypotenuse of that triangle using
Pythagorean Theorem and figure out the angle using tangent. Then using that angle, you must
figure out the resultant angle. Then, simply add 180 to that angle and that’s the final angle of the
equilibrant. After the experiment, we concluded that we could use the trigonometry way instead
using a force table every time.
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Introduction: In this experiment, we performed three trials to try figuring out the equilibrant
using trigonometry. A certain physics teacher who accidently drops bricks off of buildings to kill
students gave us two angles with the force applied to each angle. For the first two trials, we did
the trigonometry first, then we checked our calculations by testing it with a force table.
Fortunately, the calculations added up and the ring was balanced in the middle of the force table.
For the 3rd trial, we did not use the force table and only used trigonometry. There are three major
ideas that play part in this experiment: Newton’s 2nd Law, Newton’s 3rd Law, and vectors.
Newton’s 2nd Law helps us figure out the amount of force applied to the angle. The given mass
would be multiplied by 9.8 which gives you the force. Newton’s 3rd law states that for every
action, there is always an equal and opposite reaction. This applies to this lab because to
neutralize the resultant angle, there must be an equal amount of force pulling in the exact
opposite direction. That is why you add 180 to the resultant angle. Lastly, vectors show
magnitude and direction. In this lab, vectors were used multiple times to show in which way the
forces pulled the ring. For example, in trial 2, for one angle, it pulled one way and for the other
angle, it pulled the opposite way. Whichever angle had a stronger force, the ring would be pulled
more towards that direction. Also, the resultant angle pulls one way and its opposite angle pulls
the other way with the same force. It is very similar to a tug-of-war rope. When one teams pulls
one way and the other team pulls the other way with the same force, the rope won’t move; only
the tension of the rope will increase. This is why the ring in the center of the table stays exactly
where it was only raised up slightly. At the end of the experiment, we can conclude that
trigonometry can be used in place of a force table.
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Materials/Equipment: 1 force table
1 calculator
1 electronic balance
mass rings
1 pencil
Procedure: Trial 3
1. Be given two angles and two masses/forces
2. Make an x-y axis and make right triangles with given information
3. Figure out the massx and the massy of both right triangles by using sine/cosine
4. Add the massesy together and add the massesx together.
massy=132.62 + 182.19=314.81 g
massx=-364.37 + 233.19=-131.18 g
38°
295.92 g160°
20°
387.76 g
38°
387.76 g
20°132.62 g
-364.37 g (negative because it’s on left side of y-axis)
Plug in calculator:Sin(20)x387.76=132.62Cos(20)x387.76=364.37
295.92 g182.19 g
233.19 g g
Plug in calculator:Sin(38)x295.92=182.19Cos(38)x295.92=233.19
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5. Make another right triangle with the new massx and the new massy to figure out
the angle and the hypotenuse using tangent and Pythagorean theorem.
6. Figure out the actual angle where the force should be applied
Equilibrant of 2.9 N (295.92 g) @ 38°and 3.8 N (387.76 g) @ 160°:
341.05 g @ 292.62°
Data:Trial 1:
Angle Placed Angle made in right triangle
Mass applied at angle
Massx Massy
35° 35° 28 g 22.94 g 16.06 g
85° 85° 42 g 3.66 g 41.84 g
245.33° 65.33° 63.71 g 26.6 g 57.9 g
Boldface-given
0.31 g314.812 + 131.182=c2
116313.53=c2
341.05=c
Tan-1(314.81/131.18)= °67.38=°
67.38°
112.62°
112.62° is the angle in between the 38° and 160° given the forces, so to neutralize that angle with the force, there must be another force pulling back exactly opposite of 112.62° and with the same amount of force so you add 180
292.62°
0.13 g
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28 g (274.4 N)
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Trial 2: *Negative means mass was on left side of y-axis
Angle Placed Angle made in right triangle
Mass applied at angle
Massx Massy
48° 48° 31 g 20.74 g 23.04 g
152° 28° 45 g -39.73 g* 21.13 g
293.27° 66.73° 48.07 g -18.99 g* 44.16 g
63.71 (624.358 N)
295.92 g (2.9 N)
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Trial 3 (no force table used):
Angle Placed Angle made in right triangle
Force applied at angle
Massx Massy
38° 38° 2.9 N (295.92 g) 233.19 g 182.19 g
160° 20° 3.8 N (387.76 g) -364.37 g* 132.62 g
387.76 g (3.8 N)
341.05 g (471.09 N)
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292.62° 67.38° 3.34 N (341.05g) -131.18 g* 314.81 g
Data Analysis:
Trial 1-
42 g
35°
28 g16.06 g
22.94 g
85°
41.84 g
3.66 g
26.6 g
57.9 g
65.33°
63.71 g
245.33°
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Equilibrant: 63.71 g @ 245.33°
Trial 2-
Equilibrant: 48.07 g @293.27
48°28° 31 g
20.74 g
23.04 g45 g
39.73 g21.13 g
66.73°
18.99 g
44.16 g
293.27°
48.07 g
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Trial 3-
Equilibrant: 341.05 g @ 292.62°
Discussion/Conclusion: In this experiment, we were trying to prove that trigonometry is a more
effective way of figuring out the equilibrant rather than using a force table. The trigonometry
38°20°
295.92 g387.76 g
233.19 g
182.19 g132.62 g
364.37 g
67.38°
131.18 g
341.05 g
314.81 g
292.62 °
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way includes making two right triangles with the angles given and then using sine and cosine to
figure out the massesx and the massesy. Once you figure those out, you add them up and you
make a new right triangle with the new numbers. After that, you use tangent and the Pythagorean
Theorem to figure out the hypotenuse and the angle. The hypotenuse is the actual force pulling at
the angle. Then, you have to figure out the angle in relation to the reference angle and you just
add 180 to that and that gives you the equilibrant. You add 180 because you have to pull in the
exact opposite direction.
References: Force table
diagram-http://titan.bloomfield.edu/facstaff/dnicolai/Physics/Physics105/Experiments/force.htm
Research- http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html
Trial 1 force table pic Trial 2 force table pic
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