What is the graphical method of studying equilibrium is done by which force
Answers
Answer:
Forces are one of a group of quantities known as vectors, which are distinguished from regular numbers (known as scalars) by the fact that a vector has two quantities associated with it, a magnitude and a direction (related to a coordinate axes of the system you are dealing with). These properties completely characterize a vector.A vector may alternatively be described by specifying its vector components. In the case of the Cartesian coordinate system (the system we will be primarily dealing with) there are two components, the x-component and y-component. These two properties also completely characterize a vector. Vectors, and in the case of this lab, force vectors, can be represented pictorially (see Fig. 1) by an arrow pointing in the direction of action of the force, with a length proportional to the strength (magnitude) of the force.

Figure 1
The components
Fx
and
Fy
in the x and y directions of the vector F are related to the magnitude F and angle θ by:
( 1 )
Fx = F cos θ and Fy = F sin θ
and conversely:
( 2 )
F = Fx2 + Fy2, and θ = arctanFyFx.
When several forces act on a point, their sum can be obtained according to the rules of vector algebra. Graphically, the sum of two forces
F = F1 + F2
can be found by using the parallelogram rule illustrated in Fig. 2 or, equivalently, by the head-to-tail method illustrated in Fig. 3.

Figure 2

Figure 3
The sum of the vectors can also be derived analytically by adding their components:
( 3 )
Fx = F1x + F2x, and Fy = F1y + F2y
Condition for Translational Equilibrium
An object is in translational equilibrium when the vector sum of all the forces acting on it is zero. In this experiment we shall study the translational equilibrium of a small ring acted on by several forces on an apparatus known as a force table, see Fig. 4. This apparatus enables one to cause the forces of gravity acting on several masses (F = mg) to be brought to bear on the small ring. These forces are adjusted until equilibrium of the ring is achieved. You will then add the forces analytically by adding their components and graphically by drawing the vectors and determining if they add to zero using the rules for the addition of force vectors listed above.

Figure 4
PROCEDURE
Equilibrium with Three Forces
We shall first study the equilibrium of the small ring when there are three forces acting on it. Two of the forces
(F1 and F2)
will be fixed and the third one
F3
adjusted until equilibrium is reached.
1
If necessary, level the force table using the small bubble level placed on the table's surface.
2
Choose any two masses you like in the range 100-300 g, and place each mass on a weight holder. Use the electronic balance to measure each of the masses including the holder. Designate the measured masses as
m1 and m2.
The uncertainty of these measurements should be limited to the precision of the balance.
3
Place the pin in the middle of the force table and place the ring over the pin. Attach two of the four pulleys provided to the force table at any position other than zero degrees. Record the value of θ1 and θ2. The uncertainty in these angles should be limited to the precision to which you can read the angles on the force table.
4
Run two of the strings (attached to the ring) over the pulleys, and suspend the masses that you have chosen at the appropriate angles
(m1 at θ1 and m2 at θ2).
The tension in the two strings acts on the ring with forces
F1 and F2,
each with a magnitude equal to the weight of the corresponding mass and holder
(m1g and m2g)
suspended at the end of each of the strings.
5
Pull one of the remaining strings in various directions until you locate a direction in which the ring is freed from the pin when you apply the right amount of force. Attach a third pulley at this position. Run the string over the pulley and attach a weight holder to the string. Add weights to the weight holder until the ring pulls away from the pin, so that the pin is not necessary to hold the ring in place. This last added force is the (equilibriant) force
F3 (m3g).
It may be necessary to make minor adjustments to the angle to obtain a precise measurement. Make sure that the strings are stretched radially and the pin is at the center of