Physics 202L- Spring 2001-  Experiment #2:       Addition of Forces by Vector Methods

The purpose of this experiment is to find the vector sum (called resultant R) of two or more vector quantities. The vectors in this case are forces applied to a central ring. The same rules apply to all vector quantities, like Velocity, Acceleration, Coulomb force, Electric fields, Magnetic force etc. Experimental verification of Vector addition for mechanical forces is applicable to all quantities mentioned here.

EQUIPMENT:

Force table, together with slotted masses (grams) and hangers, center ring, pin and strings, ruler.

THEORY

Several forces acting on an object are, in effect, equivalent to a single net force, called resultant R. If a force equal to R is applied to the object in the opposite direction, it will cancel out R, and the object will stay in equilibrium. A force equal and opposite to R is called equilibrant (say E).

Thus if an object remains at rest under the action of several forces, one of the forces will be the equilibrant of the all the remaining forces. Experimentally, this is the best way to find R as it is equal and opposite to E which is easy to find.

PRE-LAB Study:

1.    Study the algebraic method of adding vectors from your physics textbook.                                          A

2.       Consider two vectors ,  of equal length, say 10 cm.  Consider to act

along 0° and to act along 90°, 180°, 270° respectively.  Where do you

expect the resultant to be in each case?

3.       If is not equal to , but twice as large, then where would you expect the resultant to be in each of the above three cases?

PROCEDURE:

On your table in the lab, you will find a card giving you two sets of masses representing forces and their respective angles.  The force of tension in the string is equal to (mass x gravity). Take g=10 m/s2 for simplicity and enter forces in table.

1.   Fix the two pulleys at the given angles and add masses as implied in the first set.  The string should not experience friction at the pulleys and should be positioned on the ring loosely such that the string appears to come from the center pin. Do not forget to include the mass of the hanger (50g) to the added mass, then change to kg and N.

2.       Pull the third string by hand and determine the position where your pull can keep the ring exactly at the center. Fix the third pulley in this position. This is the direction of equilibrant E.

3.   Add weights to the hanger on the third pulley to find the magnitude of the equilibrant force E for keeping the ring at the center.  Record the magnitude E and the direction qE.in the table.

4.   From qE, determine the angle qR  (diametrically opposite to it) at which the resultant R of the given forces must lie. Also record R (=E)

5.   Without changing qE, gently add masses to E in steps of 1g till the equilibrium is disturbed i.e. the ring moves slightly.  Note down the additional grams as Dm.

6.   Remove the added Dm and return to mass E.  Now slowly alter the angle qE, first to the right, in steps of 1°, to reach a point where equilibrium is disturbed.  Note the change DqE which causes this.  Repeat to the left.  Note the change.  Record average of the two readings as DqE.

7.   Quote your answer for R, and qR including an appropriate error from (5) and (6) above.

8.   Repeat steps 1-7 for the second set.

9.         By algebraic method, determine the magnitudes and direction of the resultants of the two given sets of vectors.

10.        On the back of data sheet, briefly discuss the possible causes of any differences in the results from the two methods.

Physics 202L (T.Arshed)

 F1 M1(kg)xg Angle q1 Force F2 Angle q2 Equilibrant E from table M(kg)xg Angle qE MagnitudeResultant Force R Angle qR Dm DqE 1. 2.

R ± DR                                                  qR  ±  DqR

1.

2.

Algebraic Method:

1st set               F1x =                                         F2x=                                       Rx= F1x+ F2x =

F1y=                                          F2y=                                       Ry= F1y + F2y =

R = [R2x + R2y]˝ =

qR = tan-1 (Ry / Rx ) =

2nd set              Fx1=                                          Fx2 =                                      Rx = Fx1 + Fx2 =

Fy1=                                          Fy2=                                       Ry= Fy1 + Fy2 =

R = [R2x + R2y]˝ =

qR = tan-1 (Ry / Rx ) =