EXPERIMENT 3- Addition of Vectors
PHYS 1401
OBJECTIVES
When a number of vectors passing through the same point, acts on an object, it may be
replaced by a single force which is called the resultant or the sum. The resultant therefore
is a single force which is similar in effect to the effect produced by the several forces
acting on the body. It is therefore a single force that replaces those forces. The objectives
of this lab are:
1. To obtain the resultant of a number of forces acting on a body
This will be accomplished by finding the magnitude and direction of a single force
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 forces its is to replaced. 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 cosine
for the magnitude and the law of sine to find its direction in one instance. The
components method will also be used.
APPARATUS
1. Force table
2. Four weight holders
3. Four pulleys
4. Slotted weights
9. A compass
5. Strings for suspending the masses on the weight hangers
6. A ring
7. A metal pin
8. A protractor
10. Sheets of plain paper or graph paper.
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:
Ax = A cosθ
Ay = A sinθ
Ay
where θ ≤ 900 is the angle between the vector A and the x axis.
In order to find the resultant vector R of a system of vectors A, B, C, etc…
we follow these steps:
a)
Ax
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.
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 : ά = tan -1 [Ry / Rx] where ά is the angle between R
and x axis.
If ά > 0 then R is either in the 1st or 3rd quadrant
If ά < 0 then R is either in the 2nd or 4th quadrant.
EXPERIMENTAL PROCEDURE
1) Suspend a mass of 300 g over a pulley clamped at the 400 angle. Calculate the
horizontal and vertical components and set them up on the force table. Replace now
the original force with an equal force with an opposite direction to it. Check the
equilibrium of the system.
2) Suspend a mass of 100 g at 300 and a mass of 200 g at 1200. 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.
3) Keep the same masses above listed and suspend a third mass of 150 g at 2300.
Do the same thing as in procedure 2.
EXPERIMENT - Addition of Vectors
PHYS 1401
REPORT FORM
_______________________________
Name
Instructor
___________________________
Date _____________________
CALCULATIONS
1) For procedure 2, find, graphically, the magnitude and the direction of the resultant
vector.
Use the laws of sine and cosine. Show your graph and work.
2) For procedure 2, find, analytically, the magnitude and the direction of the
resultant vector.
Use the method of components.
3) For procedure 3, find, analytically, the magnitude and the direction of the
resultant vector.
Use the method of components.
EXPERIMENT - Addition of Vectors
Review Questions and Exercises
__________________________
Name
Due before lab begins. Answer on a separate sheet of paper.
Date
_________________________
__
1) Explain why several measurements were taken for each quantity.
2) Convert the volume of the aluminum cylinder into cubic millimeters and liters.
3) Find the mass of a solid brass sphere that has a radius of 4 cm.
4) In measuring the volume of the cylinders, which dimension you should be more
accurate about, the length or the diameter. Explain.
5) Why was the micrometer used instead of the vernier caliper to measure the
diameter of the wire.
6) To what decimal point can you estimate the reading on a metric ruler.
EXPERIMENT 3 – Addition of Vecrtors
Post- laboratory Questions and Exercises
_____________________
Due after completing lab. Answer in the space provided.
Name