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.
PRELAB 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/s^{2} 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 q_{E}.in
the table.
4. From q_{E},
determine the angle q_{R} (diametrically opposite to it) at which the
resultant R of the given forces must
lie. Also record R (=E)
5. Without changing q_{E},
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 q_{E},
first to the right, in steps of 1°, to reach a point where equilibrium is
disturbed. Note the change Dq_{E} which causes this.
Repeat to the left. Note the
change. Record average of the two
readings as Dq_{E}.
7. Quote your answer for R, and q_{R} including an
appropriate error from (5) and (6) above.
8. Repeat steps 17 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.
Your NAME:_______________________________ Partner’s Name:
_______________________________
Physics 202L (T.Arshed)
DATA SHEET: VECTOR
ADDITION
F_{1} M_{1}(kg)xg 
Angle q_{1} 
Force F_{2} 
Angle q_{2} 
Equilibrant E from table M(kg)xg 
Angle q_{E} 
MagnitudeResultant Force R 
Angle q_{R} 
Dm 
Dq_{E} 
1. 









2. 









R ± D_{R }q_{R }± Dq_{R}
_{ }
1.
2.
Algebraic Method:
1st set F_{1x}
= F_{2x}= R_{x}=
F_{1x}+ F_{2x }=
F_{1y}= F_{2y}= R_{y}=
F_{1y} + F_{2y} =
R
= [R^{2}_{x} + R^{2}_{y}]^{˝} =
q_{R =}
tan^{1} (R_{y} / R_{x }) =
2nd set F_{x1}= F_{x2}
= R_{x}
= F_{x1} + F_{x2} =
F_{y1}= F_{y2}= R_{y}=
F_{y1} + F_{y2} =
R
= [R^{2}_{x} + R^{2}_{y}]^{˝} =
q_{R =}
tan^{1} (R_{y} / R_{x }) =