Equilibrium: Force Table

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Abstract
Equilibrium is the condition of a system in which competing influences are balanced. In the experiment we measured and experimented for the equilibrant force, conditions and center of gravity. Our results showed consideration as to disregarding other forces than weight and tension.

1. Introduction

Equilibrium is a state of balance in which it is a condition where there is no change in the state of motion of a body. Equilibrium may be observed on objects which are at rest and also to objects which are moving at a constant velocity. Two conditions for equilibrium are that the net force acting on the object is zero, and the net torque acting on the object is zero. In the experiment done, conditions for equilibrium are observed. Equilibrant forces were determined using the force table and component methods. The unknown forces were also determined using the first and second conditions for equilibrium. Another part of the experiment was to locate the center of gravity of a composite body and to determine rotational equilibrium.

2. Theory

An object at equilibrium has none influences to cause it to move, either in translation or rotation. The basic conditions for equilibrium are: The conditions for equilibrium are basic to the design of any load-bearing structure such as a bridge or a building since such structures must be able to maintain equilibrium under load. They are also important for the study of machines, since one must first establish equilibrium and then apply extra force or torque to produce the desired movement of the machine

In the first activity, formulas used were:

Ta= (Pan A +added weight)9.8 m/s2
Tb = (Pan B + added weight)9.8m/s2

To get the Experimental Equilibrant we used the weight of the pan A plus the weight added to it.

% Error =|(Exp. – Theoretical)|*100%

In computing the Experimental Equilibrant for the second activity we used ∑F=0
Tx-T0x=0
T1cos0-T2coso=0
T1=T2

On the third activity, to get the x-coordinate and y-coordinate we used these formulas:

x=(XCWC+XSWS)/W and
y=(YCWC+YSWS)/W

On activity 4, we used these formulas:

-T1(lo/2) + Wc(lo/2 - .05) + T2(lo/2) = 0

(T1 is the reading of spring scale, lo isthe length of bar, Wc=weight of cylinder.)

3. Methodology

Materials used were force table, force board, cylinder, spring scale, electronic gram balance, card board, aluminum bar, and protractor. In the first activity: We first weighed three pans then labeled it as A, B and C. Then we hanged each of the in the force table. We then placed 100 g on pan A and 150g on pan B. We then record Ta and Tb. We balanced two tensions in the string. We then recorded magnitude and position of equilibrant and solved for the theoretical equilibrant then computed for the percent error. In the second activity: We used force board and suspended cylinder by means of two strings. We attached a spring scale to one of the strings then recorded the reading. We measure the angle on the other string using a protractor. We weighed the cylinder for the accepted value and computed for the % error. In the third activity: We used the prepared 10cm diameter square and circle. We weighed it separately and the one with the both shapes. Re determined the center of gravity using the balancing method and plumb line method. We specified position of center of gravity the checked results using the formulas given. In the last activity: We located center of gravity of the bar, hanged the cylinder 5.0 cm from the end of the bar. We drew free body diagram then used the second condition for equilibrium in determining the weight of the bar. We weighed the bar using the electronic gram balance and then computed for the % error.

4. Results and Discussion

Table 1: Equilibrant Force
TensionMagnitudePosition ( º)
Ta1.51 N30 º
Tb1.96 N200 º
E. Equilibrant0.53 N335 º
T. Equilibrant0.54 N344 º
%error1.9%
The table above shows the results for the equilibrant force,...
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