1. which method (graphical or analytic) should be used when adding vector?2. what are some of the sources of uncertainty in this experiment?AIM

To show that the sum of the forces acting on an object in static equilibrium is

equal to zero.

عالم واة

APPARATUS

Force table, pulleys, weight hangers, slotted weights, ruler, protractor

ما به

كرم الدوران

THEORY

i

If a body is in static equilibrium then (1) the sum of the forces (and torques)

acting on it must be equal to zero, and (2) the body must be at rest. Consider

a ring that has three taut strings attached to it. If the ring is held in static

equilibrium and if we represent the tensions in the three strings by F1, F2, F3,

then the sum of these forces acting on the ring must equal zero.

= i + 2 + 3 =

(1)

ΣF ,

=

i

Thus, the sum of the x and y components of the forces (in two dimensions)

must also equal zero. If we let

Ēi = Fi&i + Fly i

F2 = F2 i + F2y3

Ez = Fix it F3y

+ Fзу ј

then

Σ

Fix

=

F1x + F2x + F3x = 0

(2

2

Fiy = Fly + F2y + F3y = 0

i

5.

The magnitude of these components can be determined as follows:

MUISTA

Fix = El cos 01, F2a = |f2| cos 02, F3a = fs| cos on

Fly = | sin 01, F2y = f | sin 02,

Fзу

= |F3| sin 03

where Fi) is the magnitude of Fi (i.e., the tension in the first string) and O, is

the angle that Fi makes with the +x axis (0 is measured in the counterclockwise

direction). The components of F2 and F3 are calculated in a similar manner.

The Free Body Diagram of the ring is shown below.

у

Ę

Х

F.

F

Figure 1: Free Body Diagram of forces acting on a ring in static equilibrium. See

the text above.

مارسها السريع

PROCEDURE

1. Adjust the leveling screws at the base of the force table so that its surface is

approximately level (see Figure 2 below).

2. Set a pulley on the 0° mark of the table and suspend a 100 gram weight from

the weight hanger. Place a second pulley near the 120° mark and suspend

یکی

whes

6

دریا کی

دونی

approximately 200 grams from the weight hanger. Finally adjust the position of

the third pulley and the weight suspended from it so that the ring to which the

strings are attached is perfectly centered in the middle of the force table. The

central pin should be exactly at the center of the ring and once the central pin is

removed the ring should not move. Before taking any readings make sure that

(i) the string passes directly over the pointer on each pulley; (ii) the alignment

of each string is directed towards the centre (if it isn’t, change the position of

the knot on the ring); and (iii) the position of the ring does not change when

the apparatus is tapped.

للرا///

B.U. Instruments

Figure 2: The Force Table.

3. Record the angles and masses attached to each string. DO NOT forget to add

the mass of the weight hanger to the total mass. Estimate the uncertainty in the

mass measurement (due to friction in the pulleys) by determining the minimum

7

on a vector diagra

amount of mass that must be added before the ring moves from its equilibrium

position (the magnitude of this uncertainty should be a few grams).

4. Choose a suitable scale and add the three forces together

(see Figure 3 below. It is important to draw the diagram as accurately

so you should try to maximize the size of your diagram. Measure the resultan

of the three forces. State its magnitude and direction 0. Since the ring is in

static equilibrium the true value of this resultant should be zero. The difference

between the measured value and the true value is your discrepancy.

as possible

2

03

—

7

F3

F.

D2

length

F

angla?

Figure 3: Vector Addition (Graphical Method).

5. Calculate the resultant of the three forces by the analytic (component) method

(take the 0° line to be the +x axis). Find the discrepancy and compare it with

that found in step 4 above. On a vector diagram, draw the resultant obtained

by the graphical and the analytical methods. Which discrepancy is smaller?

CONCLUSION

1. Which method (graphical or analytic) should be used when adding vectors?

8

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