Name:_________________________________ Lab Section: _________ Group Number: __________
Lab Partners: _______________________________________________ Grade:____________
Physics 201, Lab 9
Static Equilibrium
Pre-Lab
Pre-lab Questions (turn in at start of lab)
1. In this lab, you will be using equilibrium equation to determine unknown forces. Find a third force
that can be added to the two listed so that the system remains in equilibrium. F1 = 85 N @ 63
degrees, F2 = 120 N @ 288 degrees.
2. In this lab, you will be using equilibrium equation to determine unknown forces. Find a fourth force
that can be added to the three listed so that the system remains in equilibrium. F1 = 135 N @ 155
degrees, F2 = 80 N @ 195 degrees, F3 = 185 N @ 310 degrees.
3. Find force and torque vectors that can be applied around the origin to the situation listed to maintain
equilibrium. F1 = 118 i + 48 j N @ x = 14 cm, y =-22 cm, F2 = 35 i – 72 j N @ x = 42 cm, y =16 cm.
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Name: _________________________________ Lab Section: _________ Group Number: __________
Lab Partners: _______________________________________________ Grade: ____________
Physics 201
Experiment #9
Static Equilibrium
Introduction Understanding equilibrium is of vital importance for many professions from physicists,
engineers, to physical therapists. Knowledge of where forces and torques act in any equilibrium
situation are important in determining whether a bridge will be stable or if you will dislocate
someone’s shoulder. Even though the sum of torques and forces are zero for equilibrium, the
physical situations can be quite complicated. In this lab you will get familiarity with each condition
of equilibrium in a simplified situation.
Procedure
Suppose there are three balanced forces F1, F2, and F3 as shown in Figure 1.
Figure 1. Three balanced forces.
Write down the equilibrium condition for forces in each direction. Be sure that you choose a
coordinate system to find the force components.
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The equations you have written above form the equilibrium conditions, which involves projecting
the forces on the x and y-axes. These equations are applicable to any number of forces acting in the
x-y plane.
Suppose there is a force F in the x-y plane applied along the line PM as shown in Figure 2. OM is
perpendicular to PM.
Figure 2. Torque applied about the z axis.
Write down the expression for the torque that produces a rotation around the z-axis and comment
on the direction of the torque. Note: Calculate the torque in any way you would like.
In what vector direction does the torque point in Figure 2? Explain your choice of vector
direction.
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Figure 3, shows the schematic diagram where there are four forces, none of which act along the
same line or which pass through the center of rotation. The equilibrium condition requires that the
sum of torques be zero about any point, but let us use point O as the axis of rotation.
Figure 3. Four balanced forces.
Write the expression for the sum of torques using your preferred method.
The first condition of equilibrium prevents translational acceleration of the body in any direction
and the second prevents rotational acceleration about any axis.
Equilibrium Condition 1:
In this experiment, you will apply several forces to a ring held in equilibrium at the center of the
force table. Set three pulleys at any angular position you choose. Load the weight holders until
equilibrium is achieved, with the ring no longer in contact with the screw at the center of the table.
The individual loads should not be less than 50 g or greater than 200 g. Note that the mass of each
weight holder is 5 g and must be included in all measurements.
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Equilibrium of Forces
Adjust the mass on each weight holder until the rest position of the ring is in the center of the table.
Record all three masses and the corresponding angles. Now treat one of the forces as an unknown.
Use the equilibrium of forces to find the unknown force using the other forces. Show all of your
algebraic work below and be sure to calculate the percent difference between the calculated and
measured vector.
Now use a vector diagram of the three original forces as an independent check on the sum of
forces. Draw the forces on a blank sheet of paper, using a protractor and a ruler. Choose a scale
that will allow the head-to-tail diagram to cover most of the paper. Do the three forces add up to
zero? (Does the sum-of-forces path take you back to the origin?) Discuss your results.
Part II. Four balanced concurrent forces.
Repeat the general process of Part I using four pulleys and the following prescribed angles and
masses. In a moment, you will three weight holders at   90, 180 , and 270 using masses of
about 50 g, 50 g, and 100 g, respectively. Using only paper and pencil, determine where a fourth
weight holder (somewhere in the first quadrant) and what mass will balance the ring. That is,
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calculate the x and y components of the three vectors, the magnitude and direction of the vector
(F1 + F2 + F3), and determine what F4 will balance the ring. Experimentally check your results.
Record all four masses and the corresponding angles. Do the theoretical and experimental results
match? Calculate the percent differences between your experimental and theoretical F4 vectors.
Draw a vector diagram for the four original forces on a blank sheet of paper, using a protractor and
a ruler. Choose a scale that will allow the head-to-tail diagram to cover most of the paper. Discuss
your results.
Equilibrium Condition 2:
Remove the weight holders, the strings and the ring. Leave the center screw. Place three steel balls
on force table about 3 cm from the edge at angles of your choosing. It helps to coat the steel balls
with petroleum jelly to keep them from rolling away.
Use a scissors to trim a piece of paper to the same size as the disk with holes. Fold the paper along
the dotted line and cut out a 2-cm center hole. Place this sheet on top of the plate. Insert the four
small screws by punching through the paper, into four of the small holes in this plate. The holes
which are used should be randomly distributed. Position this plate over the centering screw and
on top of the three steel balls.
Distribute four pulleys around the force table so that there is one in each quadrant of the circle.
Rotate the pulleys up so they are higher than the plate. Attach a string to each screw, run the string
over the nearest pulley, and hook it on to a weight holder.
Add weights keeping the total mass on each string within the range of 50 g to 200 g. Adjust the
masses and the pulley positions until the disk is held in equilibrium at the center of the table. To
minimize sideways forces from the pulleys, each pulley must be oriented so that its groove is
aligned with the string passing over it. When you are near equilibrium, remove the center screw
and look down the hole. Move the top plate slightly, release it and it will return to the center.
In order to record the direction of each force, make a short line near the edge of the paper and
immediately under each string. Label them 1-4 and label the corresponding small screw. Observe
the mass on each string and record its value near the edge of the paper at the appropriate position.
Restore the equipment to the situation at the beginning of Part I. That is, rotate the pulleys back to
their lower positions, remove the plate, the steel balls, and the paper. Replace the centering screw,
the small plastic ring, three strings and three pulleys.
Each member of the group should have a copy of the paper. This may be accomplished by photocopying or tracing over the original.
Refer to Figure 3. On your copy of the record sheet, carefully draw in the lines of action of the
forces and indicate the direction of each force. Choose a convenient point to serve as the pivot
point O. Choose a method for evaluating the torques and include a table containing the data and
the calculated results. For each force, tabulate the mass, force (in N), and torque (in N-cm). Be sure
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Equilibrium of Forces
to include a sample calculation which demonstrates your method of calculating torque. Determine
the sum of the four torques of which should be near zero. Discuss your results.
Post-lab Questions:
1) What was the objective of this lab? Do you feel the objective was appropriately
achieved? Why or why not?
2) Name the two most significant sources of scientific error in this experiment (Be specific
– do NOT say, for example, “human error” or “equipment limitations”). Are these errors
likely to be random or systematic? Explain.
3) Describe some ways that the error in this lab could be reduced, including the possible
purchase of additional equipment.
4) Of the methods used in this lab, graphical, experimental, and theoretical (using
calculations only), which is the most accurate? Use data/results from the experiment to
explain your assertion.
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