Experiment 3: Conditions for Equilibrium

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1. Introduction
When we say equilibrium, it is a state of balance. It is a condition where there is no change in the state of motion of a body. Equilibrium also may be at rest or moving within a constant velocity. A simple mechanical body is said to be in equilibrium if no part of it is accelerating, unless it is disturbed by an outside force. 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. Thus, the following objectives were emphasized in this experiment: to determine the equilibrant force using the force table and the component method, to determine the unknown forces using the first condition and second conditions for equilibrium, to locate the centre of gravity of a composite body, and to demonstrate rational equilibrium.

2. Theory
Equilibrant is equal in magnitude to the resultant but oppositely directed. The first condition of equilibrium is when a body at rest or moving with uniform velocity has zero acceleration. The center of Gravity is the point where the weight of a body is assumed concentrate. The second condition of equilibrium is satisfied when the sum of all torques acting on an object about any axis equals zero. In activity 1,

TA or the tension acting on the string is the weight of the pan A plus the weight added to it and multiplied to 9.8 m/s2 TB or the tension acting on the string is the weight of the pan B plus the weight added to it and multiplied to 9.8 m/s2

Experimental Equilibrant is the weight of the pan A plus the weight added to it.

Theoretical Equilibrant=

% Error = Exp. – Theoretical X 100
Theoretical

In activity 2, the equation
T1 - T2 cos Ѳ = 0 was used.
From the equation, was derived to get the value of T2 where, T1 is the reading on the spring scale when the pin is exactly at the middle of the ring Θ is the angle of the string makes with the horizontal

Experimental Weight = T2 sin Ѳ
Theoretical Weight=
% Error = Exp. – Theoretical X 100
Theoretical
In activity 3, to check the results, the actual computation of center of gravity was used.

Where XC and YC are the coordinates of the center of gravity of the circle, XS and YS are the coordinates of the center of gravity of the square, and are the coordinates of the center of gravity of the composite figure.

In activity 4, the equation was used, where,
X1 is the length of the cylinder used
X2 is the length of the center of gravity of the cylinder.
And X3 is the length of the cylinder minus the 5.0 cm.

3. Methodology
There are 4 different kinds of activity in the experiment to determine the conditions for equilibrium. The materials used were the following: Force table and accessories, force board, cylinder of unknown weight, spring scale, electronic gram balance, card board, aluminum bar, cylinder of unknown weight, and protractor. For activity 1, the group used a force table, its three pans and accessories. The three pans were weighed and labeled as A, B and C. Pan A was hung at 30 degree mark and a 100g was placed on it whereas on pan B a150 g was placed and was hung at 200 degree mark. The group balanced the two tensions in the strings by placing weight on the pan C or adjusting its position in the force table to obtain the magnitude and position of the equilibrant. The theoretical equilibrant of the two tensions was solved using the component method. The group then computed the % error using the values obtained by the component method as your accepted value for magnitude as well as direction. Figure 1: Set-up for activity 1

For activity 2, a cylinder of unknown weight was suspended on the force board by means of two strings. A spring scale was then attached to one of the strings. One member of the group pulled the string horizontally until the pin was exactly at the middle of the ring. The reading on the spring scale was recorded as T1. Another member of the group...
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