Polygon of Forces Essay

Inactive equilibrium of forces was investigated through the usage of different weights attached to cords which were connected to a cardinal ring. while blocks supported them. This assembly facilitated the force set system to show that equilibrium will be achieving irrespective of perturbations. However. due to mistakes in the experiment. the amount of the ten and y constituent did compare to zero as predicted. The graphical solution of the experiment output a polygon that is completed bespeaking that all the forces are in equilibrium while the analytical solution indicates a attendant force of 0. 088N ± 0. 181.

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Table 1: Screening symbols and significances used in the experiment.

Aim

• To analyze inactive equilibrium while legion concurrent forces is moving.

• To corroborate whether the end point of the force system of forces moving on a organic structure at remainder equates to zero or non.

Introduction/theory

A atom is said to be in equilibrium when the vector amount of the external forces moving on a point is zero. The analysis of atoms in equilibrium is based on Newton’s 1st jurisprudence of gesture. Which states that every object in a province of unvarying gesture tends to stay in that province unless acted upon by an external imbalance force. When a organic structure remain in a unvarying province of gesture the amount of all the forces moving on it is zero and it is in equilibrium.

Coplanar force systems have all the forces moving in one plane. They may be concurrent. parallel. non-concurrent or non-parallel. Almost any system of known forces can be resolved into a individual force called a attendant force. The end point is a representative force which has the same consequence on the organic structure as the group of forces it replaces. It can be determined both diagrammatically and algebraically. The graphical methods are parallelogram and triangular while algebraically the end point is the root of the summing up square of the assorted forces along their single axis. It is of import to observe that for any given system of forces. there is merely one end point.

Forces can move upon a stiff organic structure and besides a atom in the same manner. A atom has negligible dimensions and undergoes merely translational gesture while a stiff organic structure is one of definite form and size. A stiff organic structure will undergo negligible alteration when a force is applied and it undergoes both translational and rotational gesture. However. both will be in equilibrium if the summing up of the forces moving on them is equal to zero.

?F =0 ; ?Fx i + ?Fy J =0

For this vector equation to be satisfied. the force’s in x and y severally must be equal to nothing. Hence ;

?Fx = 0. ?Fy =0

When carry oning an analysis on a stiff organic structure the first measure is to make a free organic structure diagram on the system. The stairss in making this are as follows:

1. Choose the appropriate organic structure with the coveted unknown in head and pull an defined form ( study ) .

2. Bespeaking on this study all the forces that act on the organic structure including the reactions if any.

3. Identify each force ; the forces that are known should be labelled with their proper magnitudes and waies. Letterss are used to stand for the magnitudes and way of the forces that are unknown.

Figure 1: Coplanar force system

Apparatus

1 ) Forces band

2 ) Tripod base

3 ) Cord. mixture of weight hangers

4 ) Weights

Weight of hangers: A =B=C=D=E=45. 4g

5 ) Pulling paper and pollex tacks

6 ) Protractor

? Manufacturer- Oxford/Helix

? Material- plastic

? Least count- 1o grade

? Subsystem

a. Feeling element- seting the graduated table taging on the instruments to line up with the horizontal

B. Signal modification-the designation of the marker that the pulling force lines up with

c. Indicator or recorder- numeral value above the marker that it is being lined up with

Diagram

[ movie ]

Figure 2: Screening assembled setup

Procedure

1 ) The setup was assembled as illustrated in figure 2 above and the weights of the airdocks recorded.

2 ) Pulling paper was so placed on the board behind the system and a degree was used to guarantee that the full setup is aligned.

3 ) The Centre of the system was noted and it was disturbed to verify equilibrium.

4 ) Assorted weights were so added to the airdocks on the system and it was
disturbed one time more.

5 ) After the system came to rest. the points of intersection of all the cords were marked. Two points were besides marked behind each cord to depict the line of action of the hanger.

6 ) Perturbation was so applied to the system in order to look into equilibrium as the line of action of the airdocks should cover the original points marked.

7 ) The values of the weight on each airdock were recorded.

8 ) After which. the careworn paper was removed and the points obtain were connected.

9 ) The protractor was used to mensurate the angles between the forces and the horizontal ( i. e. ?. ?. ?. and ? ) and this was recorded in table 2.

Consequence

|Force ( N ) |Angle ( O ) ( with regard to |X-component ( N ) |Y-component | | |horizontal ) | | | |F1 |1. 77 |37o |-1. 41 |1. 06 | |F2 |1. 08 |28o |-0. 953 |-0. 507 | |F3 |1. 08 |90o |0 |-1. 08 | |F4 |1. 18 |30o |1. 02 |-0. 590 | |F5 |1. 77 |37o |1. 41 |1. 06 | |Fx= -1. 41 – 0. 953 + 0 + 1. 02 + 1. 41= 0. 067 | |Fy= 1. 06 – 0. 507-1. 08 – 0. 590 +1. 06 = -0. 057
| |R= 0. 0880N |

Table 2: Consequence obtained from the experiment conducted.

|Force ( N ) |Angle ( O ) ( with |Cos |X-component ( N ) |Sin |Y-component ( N ) | | |respect to | ( Angle ) | | ( Angle ) | | | |horizontal ) | | | | | |F1 |1. 77 |37o |0. 799 ± 0. 025 |-1. 41 ± 0. 044 |0. 602 ± 0. 025 |1. 06 ± 0. 044 | |F2 |1. 08 |28o |0. 882 ± 0. 025 |-0. 953 ± 0. 027 |0. 470 ± 0. 025 |-0. 507 ± 0. 027 | |F3 |1. 08 |90o |0 ± 0. 025 |0 |1 ± 0. 025 |-1. 08 ± 0. 027 | |F4 |1. 18 |30o |0. 866 ± 0. 025 |1. 02 ± 0. 029 |0. 5 ± 0. 025 |-0. 590 ± 0. 029 | |F5 |1. 77 |37o |0. 799 ± 0. 025 |1. 41 ± 0. 044 |0. 602 ± 0. 025 |1. 06 ± 0. 044 | | | |Fx= -1. 41 ± 0. 044 -0. 953 ± 0. 027+ 0+ 1. 02 ± 0. 029+1. 41 ± 0. 044 = 0. 067±0. 162N | | | |Fy= 1. 06 ± 0. 044 -0. 507 ± 0. 027 -1. 08 ± 0. 027 -0. 590 ± 0. 029 + 1. 06 ± 0. 044 = -0. 057 ± 0. 190N |

Table 3: Consequence obtained from uncertainness computations

Calculation/Equations Used:

Summation of Forces ( in equilibrium ) : ?Fx= 0 ; ?Fy= 0 ; FR = [ movie ]

Uncertainty in Resultant = [ movie ] ; Where [ movie ] = [ movie ] x ( 2 Ten )
and [ pic ] = [ movie ] x ( 2 Y )

X-component =Force*cosine of the angle

Y-component= Force* sine of the angle

R= v ( Fx2 + Fy2 )

Scale used:

1cm-0. 196N

Discussion

The consequences obtained in this experiment showed that mistakes were associated with the values. The system was in equilibrium as when it disturbed it returned to its original place. Therefore the mistakes may hold been caused by experimenter. the setup and external environmental conditions which gave the attendant 0. 0880N alternatively of nothing ( 0 ) .

Clash in the block could hold hindered the smooth gesture of the cords while the affiliated multitudes tried to keep equilibrium. therefore ensuing in the inaccuracy in the angles. Parallax mistake is a major cause factor for the inaccuracy of the consequences obtained. The points that were placed on the pulling paper behind each cord may non hold been precisely behind the single cord as there was a important spread between the paper and the cord. A 3rd signifier of mistake that could hold caused inaccuracy is environmental conditions. During the experiment the force board was subjected to interference. as the experimenter caused some sum of quiver which shifts the board.

Regardless of the many precautional steps made. the mistakes were ineluctable ; nevertheless. the experiment was conducted in recognized manor as the end point was close with a little grade of uncertainness.

Decision

Coincident forces intersect at one common point. the end point of these forces in the system moving on a organic structure at remainder equates to zero. However. the experimental values obtain for the attendant force is ( FR = 0. 0880 ± 0. 181 N ) . which was calculated form amount of Forces in X way and Y way severally.

Recommendation

It is recommended for this experiment to be more effectual in future probe and for verification of theories. that block be situated so that the distance between the cords and the board are nearer. This will cut down the mistakes that will be probably caused by parallax and quiver. A drum sander force board can be used to cut down any negative impact that it can hold on the experiment. I would besides urge reiterating the experiment several times each clip upseting the system and guaranting that the cords line up precisely with the lines of action before taking the paper from the force board.

Sample Calculation

Force 1

Summation of Forces ( in equilibrium ) : ?Fx= 0 ; ?Fy= 0 ; FR = [ movie ]

+>F1x = 1. 77Nx Cos37? = -1. 41 N

+^F1y=1. 77Nx Sin 37?= 1. 06N

% Uncertainty – Cos 37? = ( 0. 025/ Cos 37? ) x 100

= 3. 1 %

Uncertainty in F1x = 1. 41 N x 3. 1 % = ± 0. 044

F1x = – 1. 41 ± 0. 044 N

% Uncertainty in Sin 37? = ( 0. 025/ Sin 37? ) x 100
= 4. 2 %
Uncertainty in F1y =1. 06N ten 4. 2 %
= ± 0. 044

F1y = 1. 06 ± 0. 044N

Uncertainty in Resultant = [ movie ]

Where [ movie ] = [ movie ] x ( 2 Ten )
= [ movie ] x 2 1. 06

= 1. 20
and [ pic ] = [ movie ] x ( 2 Y )
= [ movie ] x 2 ( 1. 41 ) = 1. 59

Attendant Uncertainty=
[ movie ]

= 0. 0330
F1= 1. 16 ± 0. 876

x

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