# Experiment 3

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Experiment 3: Conditions for Equilibrium

Dino Tan, Nicole Ticzon, Hazel Trias, Grace Yamson

Department of Biological Science

College of Science, University of Santo Tomas

España, Manila Philippines

Abstract

In this experiment, we tackle the subjects that are the Equilibrant Forces, the Two Conditions for Equilibrium, the Center of Gravity and Torque. By using the force table, weights, force board and the different accessories, we study the effects of gravity on the instruments.

1. Introduction

Equilibrium simply means balance. In physics, it is defined as the state of body in which there is no change in motion. That is, the net force and net torque on the object is zero in all directions. There are two conditions that must be met for equilibrium.

The first condition of equilibrium states that the net force action on the object must be zero. The second condition involves avoiding accelerated rotation. A rotating body or system can be in equilibrium if its rotation rate is constant and remains unchanged by the forces action on it.

Torque is defined as the tendency to produce change in rotational motion. That is, the line of force from the right is applied to the top of the object, and the line of force from the left to the bottom.

The center of mass or center of gravity is a property of three-dimensional bodies wherein it appears to carry the entire weight of the body. The position of the center of gravity of an object affects its stability.

In this experiment, the students should be able to determine the equilibrant force using the force table and component method, to determine unknown forces using the first condition and second conditions for equilibrium, to locate the center of gravity of a composite body, and lastly, to demonstrate rotational equilibrium.

1. Theory

In activity 1, the concept of equilibrant force was apply. To compute for the coordinates of the resultant force, the x and y-component method was used. Specifically, substitute the variables by using the given conditions of the experiment.

 x y [pic 1] TA cos 30° TA sin 30° [pic 2] TB cos 30° TB sin 30° [pic 3] ? ? [pic 4] [pic 5]

To find the magnitude of equilibrant, this formula was used:

[pic 6]

Where  and are the total value of x and y-component, respectively.[pic 7][pic 8]

The resultant’s position or angle was calculated using this formula:

[pic 9]

To find for the other unknown vector, this formula was used

[pic 10]

[pic 11]

to derived the following equations:

[pic 12]

[pic 13]

In activity 2, Unknown values were found by using the concept of first condition of Equilibrium. Based from these formula,

[pic 14]

[pic 15]

this equation was derived to solve for the experimental weight of the cylinder (:[pic 16]

[pic 17]

Where is the tension measured by the spring scale and   is the tension measured of the other string.[pic 18][pic 19]

Together with the experimental weight, the Percent error was computed using this formula:

[pic 20]

Where T.V and E.V are the true value and experimental value of the weight of cylinder, respectively.

In activity 3, the following equations was used to compute the center of gravity of a square and circle attached together:

[pic 21]

[pic 22]

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, and [pic 23][pic 24]

Wc and Ws are the weight of the circle and square, respectively.

In activity 4, the concept of the second condition of equilibrium was used to find the weight of the aluminum bar. Based from this formula:

[pic 25]

Where, the equation below was derived to compute for the experimental weight of the bar:[pic 26]

[pic 27]

Where is the tension measured by the spring scale, L is the lever arm of the spring scale, and Wc is the weight of the cylinder.[pic 28]

To solve for the theoretical weight of the bar, use the gram balance to get the bar mass and multiply it by 9.8 m/s2.

[pic 29]

1. Methodology

In the first activity, three pans labelled A, B and C were weighed. On the force table, pan A with 100g was hanged at 30° while pan B with 150g was hanged at 200°.  The tension acting in the string is the weight of the pan plus the weights added to the pan were recorded as TA and TB. Two tensions in the strings were balanced by adding weight on pan C and adjusting its position in the force table. The tensions were balanced when the ring stayed at the center. The position of the equilibrant and magnitude were recorded. The magnitude recorded was the weight of the pan plus the weight added. The group solved for the theoretical equilibrant of the two tensions by component method. The percent error was computed using the values obtained by component method as the accepted value for magnitude as well as for direction.

In the second activity, a cylinder of unknown weight was suspended in the force board using two strings. A spring scale was attached to one of the strings. The string was pulled horizontally until the pin on the force board was at the middle of the ring. The reading on the spring scale was recorded as T1. 𝜃 was recorded as the measurement of the angle made by the other string and the horizontal. A free boy diagram of the ring was drawn. The group solved for the tension T2 in the other string and the weight of the cylinder. The weight of the cylinder was used as the accepted value and the percent error was computed.

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