• Advance Study Assignment
1. Distinguish between scalar and vector quantities and give an example of each.
Scalars are quantities that are fully described by a magnitude or numerical value alone.
Example of scalar quantities are speed, mass, distance, and temperature. Vector quantities
are described by both a magnitude and a direction. Examples of vector quantities are
velocity, acceleration, force, weight, and displacement.
2. How are vectors represented graphically, and how are scalars and vector quantities
distinguished when written as symbols? Vectors can be graphically represented by directed line
segments. Length is chosen to represent the magnitude of the vector and the direction
represents the direction of the vector. Vectors are represented using bold face capital letters
with an arrow overhead, ex: →F, →V. Scalar uses italics, ex: F, V.
3. What is meant by drawing a vector to scale? Give a numerical example. A graphical
representation of a vector on the scale of graph. It is a reference number used to fit the graph on
the scale. For example: 1 unit = 1 cm, or 1 m will be represented as 1 cm.
4. Why is the triangle method called the head-to-tail method? It is called the head-to-tail method
because we are drawing the given two or more vectors in such a way that head of the 1st vector
joins with the tail of the 2nd and so on, then the vector joining the tail of the 1st vector with the
head of the last vector gives us the resultant of the given vectors. The arrow is considered the
head and the origin of the vector as the tail. To add vectors, join head to tail then the resulting
vector that originates from the tail of the 1st to the head of the last. In the process a triangle is
formed.
5. How may the resultant of two vectors be computed analytically from a vector triangle? The
resultant of two vectors can be calculated by the vector parallelogram method, in which basic
property of trigonometry is used to setup a simple formula for the resultant. Let →A be the 1st
vector, →B the 2nd vector and →R the resultant.
6. How many vectors may be added by the polygon method? Are other methods of vector
addition limited to the number of vectors that can be added? Explain. The polygon method is
used for finding sum of resultant of more than two vectors. Also the head-to-tail method the
parallelogram method and method of components can be used for adding two or more vectors.
7. What is meant by resolving a vector into components? Give example. Resolving a vector means
decomposing the vector into two components when the two components are added vectorally it
gives the original vector. Example: If you pull the car with rope on an incline, you can decompose
it horizontally and vertically.
8. Briefly describe the steps in the component method of vector addition.
– Identify the velocity and angle of each other
- Resolve the vectors: Vx = V Cos θ Vy = V sin θ
- Sum up each, then solve for magnitude
- Angles can be solved by tan^-1 (Y/X) depending on its quadrant
➔ Let A and B be a vector
A = A1i + B1i
B = A2i + B2i
A + B = (A1 + A2)i + (B1 + B2)i
9. On a force table, what is the difference between the equilibrant and the resultant? Why is only
one of these actually determined experimentally? Resultant vector is a direct quantity with both
magnitude and direction. Equilibrant is a force equal to but opposite of the resultant sum of
vector forces. This force balances other forces thus bringing an object to equilibrium. The
equilibrant is determined experimentally because it is better judged experimentally. Once
equilibrant is determined, one can calculate resultant (equal and opposite).
Θ = 75 degrees
Θ = 75 degrees
.295gN
.294gN
Θ = 45 degrees
Θ = 45.6 degrees
.318gN
.318gN
Θ = 37.5 degrees
Θ = 37.2 degrees
.261gN
.261gN
.156gN
.265gN
.154gN
.267gN
Θ = 157 degrees
Θ = 160 degrees
.133gN
.132gN
T1 QUESTIONS
1. Considering the graphical and analytical methods for obtaining the resultant, which
method is more accurate? Give the probable sources of error for each method. Analytical
method is more accurate. The only source of error for analytical will come from the fact if
you are using a calculator and have to calculate the sin and cosine of an angle. With graphical
method almost every step is prone to error. Ruler is not precise, same with a compass.
Human error is also present at every point. The analytical method is the most accurate.
2. Vector subtraction (→A - →B) is a special case of vector addition, since →A - →B = →A + (→B). Suppose that the cases of vector addition I, II, and III in this experiment were vector
subtraction (→F1 - →F2).
a. What effect would this have on the directions of the resultants? (Do not calculate
explicitly. Simply state in which quadrant the resultant would be in each case. ) The
result would be in the 4th quadrant for I, II, and III. The direction of the resultant depends
on the individual components of vectors →A and →B.
b. Would the magnitude of the resultant be different vector subtraction than for vector
addition in each case? If so, state whether the subtractive resultant would be greater
or less than the additive resultant. Yes they would have different magnitudes the
subtractive resultant would be less than additive resultant. The addition has more value
than subtraction, when the vectors between →A and →B is acute.
3. A picture hangs on a nail as shown in Fig 6.7. The tension T in each string segment is 3.5 N.
a. What is the equilibrant or the upward reaction force of the nail?
Fy = Tsinθ + Tsinθ
= 2Tsinθ
= 2(3.5)sin45 = 4.95N
Horizontal component F = 2Tsin45
b. What is the weight of the picture?
W = Tsinθ + Tsinθ
= Tsin45 + Tsin45
= 4.95N
Weight = equilibrant
W = 4.95 N
The Addition and Resolution of Vectors: The Force Table
Objective:
The objective of our experiment was to obtain the mass and the degree of the resultant through
experimentation by using the force table. Once completed, we then found the sum of vectors graphically to
obtain the resultant. Next we found the sum of the vector analytically to obtain the resultant. Lastly, after
obtaining the resultant and degree we found the vector II and IV.
Procedure:
We began our procedure by setting up the force table with strings and suspended weights and performed
vector addition II and IV. Using the the two vector quantities provided for vector addition II, F1=(0.200)g N
at 20° and F2 =(0.150)g at 80°, we found their resultant by using experimental, analytical and graphical
methods. For the experimental method we set up the clamp pulleys on the force table and added the
weights to equal 200 g for F1 and 150 g for F2. We determined the third clamp pulley by adding weights
while manipulating the direction of the equilibrant force to ensure the ring was centered on the pin. Once
it was centered, we were able to obtain the mass and direction of the resultant and recorded our findings
in the data table. We repeated the same steps for vector addition IV except that it contained three vector
quantities set at 30°,90°,and 225°. We then found the magnitude and direction of the resultant and
recorded our results.
Conclusion:
Physical quantities can be generally classified as either scalar or vector quantities. Scalar quantities are
defined as only having a magnitude. Examples include speed (m/s) and temperatures (∘C). Vector
quantities have both magnitude and direction, examples are velocity, displacement, acceleration, and
force. Vectors are distinguished by using bold face capital letter with an arrow overhead. Vectors are
represented by arrows. There are three different methods that are used as vector addition, vector, triangle
and component methods. Triangle method is also known as the head-to-tail method because the tip of the
head A and the end tail B meet and can move around in the same direction. Adding vectors graphically in
the experiment involves finding the length by dividing its magnitude by the scaling factor. When drawing
the graphs using graphing paper, use a factor of two significant figures. Use a ruler/protractor to measure
the length and the direction of the angle. Magnitude is found by R scaling factor x measured length. The
vectors measured analytically are shown on the attached graphing paper.