LAB #1 FORCES IN EQUILIBRIUM
OVERVIEW:
A force is the push or pull exerted on an object. Sometimes two or more forces act on an
object at the same time. The result of this action is called the resultant force. If the resultant force
is zero, then the body experiences no net force. When this happens, the body is said to be in
equilibrium.
When several forces act on an object resulting in a net force, they may be balanced by a single
force called the equilibrant. The equilibrant exactly cancels the resultant of all the other forces,
so that the object will be in equilibrium.
Force is a vector; it has both magnitude and direction. When two forces act in the same
direction, their magnitudes are added. When they act in opposite directions, their magnitudes are
subtracted to obtain the resultant force.
When two or more vectors act on an object, and their directions are not along the same line
(same line: collinear), the resultant force is not simply the sum or difference of the magnitudes.
For example, two forces of five pounds each may act on an object with their directions 90o
different. (See the illustration below right.) The resultant
will not be as great as if they were in the same direction
(10 lbs) and it will not be as small as if they pulled in
opposite directions (zero). Also, the direction of the
resultant force will be at a 45o angle to each. Vectors may
be represented graphically in order to "add" them; both
the correct magnitude and the correct direction of the
resultant can be determined by graphical methods.
In this experiment you will place a system of forces in equilibrium. Then you will measure
the forces, and graphically add them to find the resultant. The resultant of forces in equilibrium
should be zero. If the graphical method does not give a resultant of zero, there may be an
unmeasured force in the system, probably due to friction. Also, when drawings are done
manually, the accuracy is limited.
The process of making a drawing to determine the resultant of two or more vectors is called
"adding vectors by graphical method". It is illustrated on pages 15 - 23 in the text.
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LAB #1 FORCES IN EQUILIBRIUM
OBJECTIVES:
A) Measure forces in units of newtons using a spring scale.
B) Graphically represent the magnitude and direction of a force by a vector drawing.
C) Find the resultant of several forces by adding vectors graphically.
EQUIPMENT REQUIRED:
Force Board (Disc with clamps)
Small Metal Ring
3 Spring Scales
Metric Ruler
PROCEDURE:
A) Placing forces in equilibrium
1. Place a sheet of blank paper on the force board, slipping it under the spring clips.
2. Hook the three scales to the ring, and place the ring near the center of the
board. Adjust the scales of each to read zero when they are lying flat on the board.
3. Fasten two of the scales to the board by slipping a chain link into a slot on the
outer perimeter. Choose locations/slots on the outer perimeter of the board that are
approximately 90° apart from each other. (The exact angle is not important.)
4. Fasten the third scale to an outer perimeter slot so that the forces are balanced. Adjust
the tensions so that each scale reading is between 10
newtons and 20 newtons.
B
5. Rotate the paper underneath the spring scales so that
the bottom edge of the paper is parallel with the direction
of one of the spring scales. Refer to the diagram to the
C
A
right.
A
6. Place a pencil dot on the paper indicating the location
of the center of the ring. Put a dot under the rod of each
scale, at the point where the rod enters the scale housing. (This will allow you to draw
the direction of each vector accurately.)
7. Next to each scale, write/record the scale reading on the paper. Label the forces A, B,
and C as shown in the diagram above.
8. Remove the paper from the table, and draw light guide lines from the center
along the direction of the three forces. Draw an arrow head on each line to indicate the
direction of the pull.
9. Draw a reference line through the dot marking the center of the ring. This line
should be approximately parallel to the lower edge of the paper. Mark this
line as 0° (zero degrees). Notice that force A should be along the reference
line pointing to the right with an angle of zero degrees.
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LAB #1 FORCES IN EQUILIBRIUM
10. Using a protractor, measure the angle with the base line made by the other two force
vectors. Any arrow (vector) pointing upward will lie between zero degrees and 180
degrees. Arrows pointing downward will lie between 180° and 360°. Ask for help from
the instructor if you are not sure how to use the protractor. Mark each angle clearly next
to each arrow (vector).
B) Graphical Representation and Addition of Force Vectors
The following steps should be completed by each student individually in the student text book.
1. Make a small free-hand sketch of the force board set-up in the space provided.
2. Draw a free-body diagram in the space provided. The ring is the "free body" which
we are considering. It is not attached to anything, so it is free to move if acted on by
unbalanced forces. Since it is not moving, the resultant of all the forces acting on it must
be zero –it is in equilibrium. Follow these steps:
a) Place a dot in the center of your space to represent the ring.
b) Draw an arrow representing the approximate direction of force A. Start the
arrow at the dot. The length of the arrow is unimportant in this diagram.
c) Repeat this process for arrow B and C. Each arrow starts at the dot in the freebody diagram.
3. In the space below the "VECTOR SOLUTION DRAWING" heading, you will
construct a scaled drawing. In the lower left of the space, place a dot for the starting point
of your drawing. Draw a very light reference line-through the dot parallel to the bottom
edge of the paper. The direction of this line to the right of the dot represents zero degrees.
4. Place the protractor starting point on the starting dot. With the protractor, construct a
line in the direction of the force with the smallest angle. In this case, it should be force A
at zero degrees.
5. The magnitude of the force vector will be indicated by the length of the arrow. Use the
metric ruler to determine the length of the arrow, letting 1 cm represent 1 newton. Place
an arrow head at the end of the vector line.
6. Construct the force with the next largest angle next. The second arrow must start at the
tip of the first arrow. In order to do this, draw a very light guide line for zero degrees
(parallel to the bottom of the paper and the previous zero line) through the tip of the first
arrow. Place the protractor center at the tip of the first arrow, and draw the second arrow
in its correct direction. Be sure that you are measuring the angle from the zero degree
reference.
7. Again determine the arrow length with the metric scale. Remember that the length
must now indicate the number of newtons on the second scale’s reading.
8. Start at the end (tip) of the second arrow, and construct the third arrow in the same
manner.
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LAB #1 FORCES IN EQUILIBRIUM
Resultant of Forces
If the three forces have a resultant of zero, the third arrow should end up at the starting point. We
know that the sum of all the forces acting on the ring is zero because the ring is at rest. However,
your drawing may have some inaccuracies, or there may have been some friction forces acting
which were not measured.
9. If the third arrow does not end where the first one started, measure the resultant by the
following procedure:
a) Draw an arrow starting at the beginning of the first arrow and ending at the tip
of the third arrow. This arrow represents the resultant of the three forces.
b) Measure the magnitude of the resultant by using the metric scale. Each 1 cm of
length represents 1 newton of force. (In other words the scale for your drawing is
1 cm = 1 newton.)
c) Determine the direction of the resultant by placing the protractor at the
beginning of the resultant arrow. Remember to use the zero degrees line as the
protractor reference.
10. On your drawing, clearly indicate by labeling the magnitude and direction of each
vector, including the resultant (if any).
11. When finished, replace the force boards, scales, and rings in their paper casing.
Discuss the questions on the back of the lab forms with your partners, and fill in the
answers you agree upon. If you cannot agree on the answer to a specific question, ask for
help from the instructor.
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LAB #1 FORCES IN EQUILIBRIUM
Supervisor: _______________
Recorder:_______________Techs: __________________
OBJECTIVES:
SKETCH OF
LAB-SETUP:
FREE-BODY
DIAGRAM:
VECTOR SOLUTION DRAWING:
Start vector
addition in this
corner.
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LAB #1 FORCES IN EQUILIBRIUM
Lab #1 ANALYSIS:
1. Two horizontal forces, of 8 N and 6 N respectively, each pull on an object due East. The
resultant force is ___________
2. The equilibrant (magnitude & direction) is _________________________________
3. If the two forces of Question #1 are pulling in opposite directions, the magnitude of the
resultant is ____________
4. Two forces of 15 lb and 20 lb are acting on an object in unspecified directions. What are the
maximum and minimum magnitudes of their resultant? Explain.
______________________________________________________________________________
______________________________________________________________________________
5. When an object is at rest, or moving in a straight line at constant speed, what is known about
the resultant of all the forces acting on the object?
_________________________________________
FOR QUESTIONS #6, #7, & #9, SKETCH: 1. A DRAWING, 2. A FREE-BODY DIAGRAM,
& 3. THE VECTOR SOLUTION DRAWING.
6. A metal ring has a pull of 10 lb at 0o, 120o, and 240o with the x-axis. Find the resultant force.
7. A 10 lb weight is supported by two cords, both making an angle of 60o with the vertical. Find
the tension in each rope.
8. Questions # 6 & 7 refer to a horizontal plane and a vertical plane respectively. Compare the
two situations.
______________________________________________________________________________
______________________________________________________________________________
9. Show how a 10 lb weight supported by two cords could cause a much greater tension in the
cords than 10 lb. Explain.
_______________________________________________________________________
_______________________________________________________________________
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