Download Exp_02_-_Vector_Addition.doc

Experiment 2
Objective
1. Obtain the resultant of a number of forces acting on a body.
2. Obtain the resultant of the same forces by drawing a vector diagram to scale to find its magnitude and
direction.
3. Determine 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.
MATERIALS
1. Force table
5. Strings for suspending the masses
2. Weight holders (#4).
6. A ring
3. Pulleys (#4).
7. A metal pin
4. Slotted weights
8. A protractor
9. Sheets of plain paper and graph paper.
Review Questions and Exercises
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
30
A
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?
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Experiment 2
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 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 the y-axis respectively, as shown. Ax and Ay are called the
components of vector A and are given by:
Ax = A cosα
Ay = A sinα α (≤ 900) is the angle vector A makes with the x-axis.
y
A
Ay
a
Ax
x
Rx
x
y
RY
y
In order to find the resultant vector R of a system of vectors A, B, C, etc
we follow these steps:
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.
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 equilibrator force that is equal in magnitude to the resultant must act in
the opposite direction on the particle. Therefore, the equilibrator is the negative of the resultant.
PROCEDURE: 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 it is to replace.
A trial and error method will be used in the laboratory experiment.
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.
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Experiment 2
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.
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Experiment 2
Report form
Name______________
Date __________
Calculations:
1)
For procedure 1, show your calculation for the components of the vector.
2)
For procedure 2, 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. .
3)
For procedure 2, find, analytically, the magnitude and the direction of the resultant vector.
Use the method of components.
4)
For procedure 3, find, analytically, the magnitude and the direction of the resultant vector.
Use the method of components.
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?
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