Static Equilibrium
Pre-Lab Question
UM Physics Demo Lab 07/2013
Can an object that has multiple forces acting on it remain at rest? Explain your
reasoning.
EXPLORATION
Exploration Materials
3 spring scales (Ohaus 20N/2000g)
1 one inch diameter split ring
1 2’x2’ perforated board
3 tool hooks to fit perforated board
1 set of ten ½ inch cut steel washers (standard weights)
3 Clear plastic rulers (1 per person)
10 Xeroxed coordinate grid sheets
1 yardstick
1 steel gusset (angle bracket)
3 sharp pencils (1 per person)
Special Note
This activity requires good technique to achieve good results. Trace your
directions from the scales carefully—small errors in angle can produce large
errors in distance. When tracing vectors from one page to another, be very
careful that the two pages are not rotated relative to each other—the top and
sides of the two pages must remain parallel to each other. You will find that
your ninety-degree angle tools are very helpful for this. Finally use the
centimeter scale on your clear ruler to accurately draw the length of each vector.
Vector Addition
1. Pull on the ring with three scales and attach the wire loops at the top of the scales
to the perforated board with the wire hooks provided to keep the scales under
tension. For your vectors to fit on the coordinate grid the largest scale reading
should not exceed 16 N.
2. Slide one of the preprinted coordinate grid sheets under the scales and align the
ring with the circle in the center of the page. Rotate the paper so that the scale
with the largest reading lies along the –y axis of the paper (remember, this
reading must less than or equal to 16 N). Tap the face of each scale gently to
ensure that none of the pointers are stuck and then carefully and accurately
trace under each scale’s hook with a sharp pencil to establish the direction each
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scale is pulling on the ring. Label each direction line with the reading on the
corresponding scale.
3. Using the clear ruler, extend the direction lines you traced from the coordinate
origin to the edge of the page. If the lines you traced will not pass through the
origin, carefully move the clear ruler so that it is parallel to the line you traced
and draw a line that will pass through the origin to the edge of the page.
4. Each group member should now make a personal tracing of this master data page.
Simply lay a fresh coordinate grid sheet over the master sheet and make a dot that
lies along each direction line. Draw the direction lines from the origin, through the
dot to the edge of the page and copy the scale readings next to each direction line.
This can be done very quickly. One group member should label the group’s master
tracing as “Original Data Tracing” and keep it in his/her lab notebook.
Each group member should now perform the remaining analysis using their
personal data sheet traced from the master copy.
5. Using the clear ruler, carefully measure from the origin a distance in centimeters
equal to the scale reading in Newtons and mark this distance on the direction line.
Do this for all three direction lines/scale readings. Draw an arrow head on each
direction line ending at each distance mark. You have now represented the three
vector forces pulling on the ring as arrows with their tails at the origin; the length
of each arrow in centimeters equals the scale reading in Newtons. Your traced
data sheet should now look like this (the scale reading labels are not shown in this
cartoon):
To make it easier to talk about our data and analysis, let’s all agree to label the three
vectors as shown so we all mean the same thing when we refer to vectors A, B and C.
6. Now add these vectors “tip to tail”. To do this, place a fresh coordinate grid sheet
over your data sheet with the coordinate axes of the two sheets perfectly aligned.
Draw a dot at the tip of vector A (you can make it an arrow head if you like).
Draw a line from the origin to your dot and you have made a copy of vector A on
your top sheet. Now slide the top sheet so that the tip of vector A (your dot) is at
the tail of vector B (the origin) and mark a dot or arrowhead to mark the tip of
vector B on your top sheet. Draw a line to connect the tip of vector A with your
new dot and you have drawn a copy of vector B “tip to tail” with A. Repeat the
process one more time to place the tail of vector C at the tip of vector B. You have
now pictorially added vectors A, B and C. Label the vectors in your drawing
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according to our convention. An arrow drawn from the tip of vector C to the tail of
vector A therefore represents the vector sum A + B + C.
7. What is the state of motion for the ring with the three scales pulling on it?
8. What type of physical quantity do the vectors A, B, C that we have constructed
represent?
9.
The vector sum of all forces acting on a body is called the net force. For a body
to remain at rest, the net force acting on it must be zero. How long should
the arrow be from the tip of vector C to the tail of vector A in your vector addition
drawing, given that the ring is not moving?
10. Considering your answer to question 9, where in your coordinate grid should the
tip of vector C be located if this experiment has worked perfectly?
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11. Considering your answer to question 10, give your assessment as to how well the
experiment worked.
12. Discuss two possible sources of inaccuracy that could have affected the results of
this experiment. Be very specific. “Inaccuracy or errors in the equipment” is not a
specific enough answer. Explain how the equipment might have affected the
results.
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Torques
Build a seesaw using your yardstick and one of your angle brackets as shown below:
13. Fill in the table below by balancing the seesaw with the distances and numbers of
washers by balancing the seesaw to find the unknowns in the table. N1 and N2 are
the number of washers in each stack of washers balanced on the seesaw. The
distances D1 and D2 are measured to the centers of the holes in the washers.
Report your distances to the nearest even inch
N1
D1
# washers
inches
3
4
2
4
N1x D1
washer-inches
N2
# washers
inches
N2x D2
washer-inches
1
4
5
D2
8
5
14. In light of your data if N1 = 6 and D1 = 4 inches, predict the distance D2 to place
a stack of N2 = 3 washers to balance the seesaw.
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15. Now balance the seesaw with the washers and distances from question 15. Was
your prediction correct? What value of D2 actually balances the seesaw?
16. State a relationship between N1, D1, N2and D2 which must be true for the seesaw
to balance.
17. The product of vertical force and horizontal distance to the seesaw fulcrum is the
magnitude of a torque vector which points into the page at the fulcrum if the
seesaw rotates clockwise under the action of the force and out of the page at the
fulcrum if the seesaw rotates counterclockwise under the action of the force. For a
seesaw to balance without rotating, the net torque (vector sum of all
torques) about the fulcrum must be zero. Does a balanced seesaw satisfy this
condition? Explain your reasoning (Hint: textbook Chapter 2.1).
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Everyday Applications
APPLICATION
1. Mechanical advantage is defined as the ability to produce a large force from a small
one. Explain how your seesaw data illustrate the mechanical advantage of a lever
and a fulcrum.
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2. We have used the convenient experimental units of #washers for weight (force)
and inches (distance) to compute torques (force times lever arm distance) in
washer-inches. The SI (MKS-meters-kilograms-seconds) unit for torque is the
Newton-meter (N-m). Using the data provided, convert one washer-inch of torque
to Newton-meters. Round your answer so as to report three figures past the
decimal point. Show your calculation in detail.
Data: Mass of one washer = 0.016 kg
Acceleration of gravity = 9.8 m/s2
1 inch = 2.54 centimeters (cm)
1 meter (m) = 100 cm
1 washer-inch = ______________ Newton-meters (N-m)
Summary:
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Vectors are added graphically by placing them tip-to-tail
The net force is the vector sum of all the forces acting on an object
For an object to be at rest, the net force acting on it must be zero.
The product of vertical force and horizontal distance on a seesaw is the magnitude
of a torque vector.
The direction of the torque vector is into the page at the fulcrum if the force
rotates the seesaw clockwise and out of the page at the fulcrum if the force
rotates the seesaw counterclockwise.
For the seesaw to balance at rest, the net torque vector at the fulcrum must be
zero.
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