EXPERIMENT 2 - Addition of Vectors
OBJECTIVES
When a number of vectors passing through the same point act on an object, it may be replaced with a
single vector which is called the resultant or the sum. The resultant therefore is a single vector which is
equal to the effect produced by the several forces acting on the body.
The objectives of this lab are:
1. To obtain the resultant of a number of vectors acting on a body. This will be accomplished by finding
the magnitude and direction of a single vector necessary to make a ring centered around a pin located
in the center of a turntable when placed on a force table along with the vectors it is to replace.
A trial and error method will be used in the laboratory experiment.
2. To obtain the resultant of the same forces by drawing a vector diagram to scale to
find its magnitude and direction.
3. Determination of the resultant using the analytical method, including the law of cosines
for the magnitude and the law of sines to find its direction in one instance. The
components method will also be used.
MATERIALS
1. Force table
5. Strings for suspending the masses
2. Four weight holders
6. A ring
3. Four pulleys
7. A metal pin
4. Slotted weights
8. A protractor
9. Sheets of plain paper or graph paper.
EXPERIMENT 2 - Addition of Vectors
Review Questions and Exercises
PRE LAB QUESTIONS
Due before lab begins.
Name______________
Date __________
1) What is the basic difference between scalars and vectors?
2) Is temperature is a vector quantity? What do plus and minus temperature signify? Explain.
3) A vector A has a magnitude of 60 m and directed as shown.
Find the x and y components of this vector.
y
x
60
4) What are, briefly, the steps to find the resultant of vectors?
5) What is the difference between a resultant & equilibrant vector & what do they physically mean?
THEORY
A vector is a physical quantity that has both magnitude and direction. Examples include force, weight,
displacement, velocity and acceleration. On the other hand, a scalar is a physical quantity that has
magnitude only, examples speed, mass, distance, temperature, population. A vector may be represented
by a letter example A→ with a bar on top indicating the direction, or by a bold letter, example A.
A vector A can be written as a sum of two vectors Ax and Ay along the x and y axis respectively, as
shown. We call them the components of vector A and are given by:
y
Ax = A cosα
Ay = A sinα
where α ≤ 900 is the angle between the vector A and the x axis.
A
Ay
a
In order to find the resultant vector R of a system of vectors A, B, C, etc…
we follow these steps:
Ax
x
Rx
x
y
a)
Find the x and y components for each vector using the above equations.
i.e find Ax, Bx, Cx ... and Ay, By, Cy ....
Remember they can be positive or negative depending on their direction.
RYy
R
q
b) Add up these components to get:
Rx = Ax + Bx + Cx + …
Ry = Ay + By + Cy + …
c) now, the magnitude of R is : [Rx2 + Ry2] ½
the direction of R is : θ = tan -1 [Ry / Rx] where θ is
the angle between R and x axis.
If θ > 0 then R is either in the 1st or 3rd quadrant
If θ < 0 then R is either in the 2nd or 4th quadrant.
For a particle to be in equilibrium, an equilibrant force that is equal in magnitude to the resultant must
act in the opposite direction on the particle. Therefore, the equilibrant is the negative of the resultant.
PROCEDURE
1) Suspend a mass of 100 g at 200 and a mass of 200 g at 1300 clockwise. Find the resultant of these
two forces by the method of components. Check your result by mounting a pulley directly
opposite to the resultant and of same magnitude; the ring should be centered.
2) Keep the same masses above listed and suspend a third mass of 150 g at 2500 clockwise
Do the same thing as in procedure 2.
REPORT FORM
Name______________
Date __________
CALCULATIONS
1)
For procedure 1, find, graphically, the magnitude and the direction of the resultant vector.
Use the laws of sine and cosine. Show your graph to scale on a separate sheet, if needed. .
2)
For procedure 1, find, analytically, the magnitude and the direction of the resultant vector.
Use the method of components.
3)
For procedure 2, find, analytically, the magnitude and the direction of the resultant vector.
Use the method of components.
EXPERIMENT 2 - Addition of Vectors
REPORT FORM
Name______________
Date __________
POST LAB QUESTIONS.
1) State in your own words what your conclusion is from this experiment.
2) What are the main roles of the pulleys? Explain.
3) Can the ring be in equilibrium while all the forces acting on it lie in two adjacent plane? Explain.
4) State the condition for translational equilibrium of a particle.
5) What are some possible sources of error?