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I'm working on a physics case study and need a sample draft to help me understand better.

can you help answer those questions and I already uploaded the file in below. thank you!

FORCE VECTORS
Purpose
The purpose of this experiment is to familiarize the student with some elementary vector concepts and
to determine the resultant of some concurrent, coplanar forces.
Theory
A vector is a quantity that has both magnitude and direction. For instance, a force of 10 lb upward or
a velocity of 30 miles per hour east is a vector. A scalar is a quantity that has magnitude but not
direction. For instance, temperature and volume are scalars, since it would make no sense to speak of a
temperature of 70 ยฐF west or a volume of 20 cubic feet south. The resultant of two or more vectors is the
single vector that could be substituted for the given vectors and have the same effect. Although there are
many types of vectors, this experiment will concentrate on force vectors and their resultants.
Suppose that a 3 lb force is acting on a body in an easterly direction and a 2 lb force is acting on the
body in a north-easterly direction as in Figure la. The 3 lb force by itself would cause the body to
accelerate toward the east; and the 2 lb force by itself would cause the body to accelerate toward the
northeast. If both of these forces (and only these two forces) act on the body, the body will accelerate in
an intermediate direction as shown. A single force R could produce the same acceleration. See Figure lb.
Since R is a single vector having the same effect as the given vectors, R is the resultant of the given
vectors.
Figure 1
Resultant of Two Forces
The magnitude and direction of the resultant of two given vectors can be predicted theoretically by
drawing a parallelogram to scale. This technique is demonstrated in Figure 2 for the forces previously
described. In the absence of other drafting tools, the parallelogram can be constructed with a compass
and ruler as shown in Figure 3.
Figure 2
Resultant by the Parallelogram Method
Often, several forces act on a body and cancel each
other out, so that the body remains in equilibrium. A
body is said to be in mechanical equilibrium if it is
remaining at rest or if it is moving in a straight line at a
constant speed. This experiment will be restricted to
the case of a body at rest under the action of three
concurrent, coplanar forces. (By โconcurrent" forces, it
is meant that their lines of action intersect at a single
point when extended. This condition insures that the
forces do not cause the body to rotate. By "coplanar"
forces, it is meant that they lie in a single plane. This
restriction permits a simpler analysis.)
Figure 4 is a sketch of the force-board apparatus to be
used in this experiment. Three spring balances apply
three forces to a metal ring near the center of the force
board. The balances tend to adjust themselves, so that
the metal ring comes to rest and remains at rest. The
chains attached to the spring balances can be fastened
to the slots in various ways to provide some control
over the magnitudes and angles of the forces.
Figure 5 is a vector diagram of the three forces acting on the ring of the force board. The resultant of
all three forces must be zero, if the ring is to remain at rest. Let us begin by finding R 12, the resultant of
F1, and F2, as shown in Figure 6. R12 can be substituted for F1, and F2, as shown in Figure 7; and the
effect should be the same. Thus, R12 and F3 in Figure 7 are equivalent to the original three forces. If R 12
and F3 are to cancel each other out in their effect on the ring, they must be equal and opposite.
F3 can be called the equilibrant of F1 and F2, since it permits the ring to remain in equilibrium while
being acted upon by F1 and F2. In general, the equilibrant must be equal in magnitude and opposite in
direction to the resultant of all other forces acting on the body.
Experiment:
Helpful site: https://www.mathsisfun.com/algebra/vectors.html
Objectives:
โข
โข
1.
The student will be able to differentiate between scalar quantities and vector quantities.
The student will be able to resolve vectors into its components.
Classify the following quantities to either scalar quantity or vector quantity by highlighting the correct
answer:
Weight
Scalar
Speed
Scalar
Mass
Scalar
Acceleration
Scalar
Vector
Vector
Vector
Vector
Density
2.
Scalar
Vector
Distance
Scalar
Vector
Force
Scalar
Vector
Volume
Scalar
Vector
Find the magnitude and direction of the resultant force of F1 and F2 by filling the table. The
magnitudes and directions of F1 and F2 are given.
Force
Magnitude of force
Direction (ฮธ)
XYcomponent
component
F1
44
28
F2
17
106
Resultant
The magnitude of the resultant force is:
The direction of the resultant force is:
3.
Find the magnitude and direction of the resultant force of F1, F2, and F3 by filling the table. The
magnitudes and directions of F1, F2, and F3 are given.
Force
Magnitude of force
Direction (ฮธ)
X - component
Y - component
F1
0.77
100
F2
0.61
30
F3
0.43
156
Resultant
The magnitude of the resultant force is:
The direction of the resultant force is:
4.
Vectors addition using PhET Interactive Simulations:
https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html
Consider vector ๐โ and vector ๐โ are force vectors, and vector ๐โ is the resultant vector.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
Click on the link shown above and select โExplore 2Dโ option window at the bottom of the graph.
Drag the origin of the graph paper to the middle.
Click on vector segment ๐โ and drag it so the tail positioned at the origin of the graph.
Adjust vector ๐โ to a magnitude 6 N, and the angle ฮธ = 30.0ห.
Drag vector segment ๐โ to the graph so the tail at the origin.
Adjust vector ๐โ so the magnitude is 5 N, and the direction with angle ฮธ = 90.0ห.
Add the two vectors graphically using the head to tail method.
Click on the sum vector where ๐ โ = ๐โ + ๐โ .
Write the magnitude and the direction of the sum vector (resultant) ๐ โ .
Use the magnitudes and directions of the added vectors to calculate the magnitude and direction of the
resultant vector ๐ โ using the analytical method.
Magnitude of vector
Direction (ฮธ)
๐โ
6
30
๐โ
5
90
Vector
๐ โ
X- component
Y- component
What is the magnitude and direction of vector ๐ โ ?
To make the system at equilibrium, an equilibrant force ๐น๐ธ should be applied, what is the magnitude and
direction of ๐น๐ธ ?
5.
Calculate the magnitude and direction of the resultant force of the forces given in the figure below:
6.
What is the relation between the resultant force and the equilibrant force?
...

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