Equilibrium of a Rigid Body
PURPOSE: To investigate the conditions of equilibrium of a rigid body; to look at several
different static examples.
INTRODUCTION: In order for a body to be in a state of static equilibrium, the following must be
true:
(1) The vector sum of all the forces acting on the body must be zero.
(2) The vector sum of all the torques about any axis must be zero.
Part 1. Equilibrium of a Meterstick: The principles of equilibrium can be demonstrated using a meter
stick that is suspended by string, as shown in the illustration. When a force or system of forces is
applied, torques and lever arm distances can be calculated when the object is in static equilibrium.
Equipment: force probe (used as a hook only, no computer or interface needed), meter stick, meter
stick clamp, supporting rods and
clamps, 100g mass, unknown
hanging mass, electronic scale.
1. Locating the Center of
Gravity
a. Using the electronic balance, measure the mass of the meter stick and calculate its weight.
mms _________kg
FG-ms ________ N
b. Hang the clamp from the force probe with screw pointing down. Find the center of
gravity of the meter stick to the nearest millimeter (1/10th of a centimeter) by sliding the
meter stick through the clamp until it is balanced.
Record the position of center of gravity___________ m (change from cm)
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2. Clamp position with a 100-gram mass
a. Draw an extended free body diagram of the meter stick in static equilibrium with a 100 g mass
hanging from the 90-cm mark. Identify all of forces acting on the meter stick.
b. Calculate the new position of the clamp in order to achieve static equilibrium. Show your work here:
Calculated position of clamp: ____________m
c. Hang the 100-g mass from the meterstick at the 90-cm mark, using a “massless” rubber band
and move the clamp so the system is in equilibrium.
Actual position of clamp _____________m
3. Determining the Value of an Unknown Mass
Temporarily remove the 100-g mass from the meter stick and re-position the support clamp at the
meter stick's center of gravity. Suspend the 100-g mass at the 90-cm mark to start. Suspend the
unknown mass from the other end, so that the system is in equilibrium. If you are unable to find
an equilibrium point with the 100-g mass at 90 cm, move it to another position.
Position of 100-g mass: ______________m
Position of unknown mass: ______________m
a. Draw an extended free body diagram of the meter stick, locate and identify the forces:
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b. Calculate the mass of the unknown, using the sum of the torques method. Show your work
here:
Calculated unknown mass. ________________kg
Now measure the mass of the unknown mass using the electronic balance.
Measured unknown mass_________________
kg
c. Find the percentage difference between calculated and measured mass. Use measured mass
for the denominator.
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Part 2: Finding the tension force and the normal force
Additional Equipment: For this part you will need the interface and computer to use the force probe.
Plug the force probe into Ch. 1. When you start up Logger Pro, use the default graph. We will be using
the setup shown below, without the meter stick clamp.
Before you set up your apparatus, please complete a-e; then see an instructor to help with setup.
a. Record the mass of the meter stick, the position of the center of gravity of the meter stick (these
are from part 1), and the calculated value for the angle θ, given an apparatus height of 0.6 meters.
Mass of meter stick: ______kg
Position of the center of gravity of
the meter stick: ________m
Angle θ : height difference between
scale and hook of force probe is
equal to 0.6 meters.
0.6 m from scale to hook
Angle θ: _________
b.. Draw an extended free-body diagram
of the meter stick, showing all forces
acting on meter stick (tape on scale can be
considered a sort of static friction force):
Scale
c. Predict whether the scale reading will be greater than, equal to, or less than the mass of the meter
stick. Explain your answer:
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d. Using the fact that the meter stick is in static equilibrium, solve for the tension force and the scale
reading (y component of force due to scale).
Calculated force probe reading: T ___________N
Calculated scale reading: n_____________N
e. Did the value of the scale reading agree with your prediction?
relationship?
If not, what is the correct
When you have finished the calculations, show them to an instructor and obtain the equipment
needed to set up this part of the experiment..
Using a meter stick, set up your system as indicated by the diagram. Use the blue tape to tape the
bottom of the stick to the scale. Make sure to zero your force probe in the correct orientation.
Measure the tension in the string with the force probe and obtain the scale reading (change scale reading
value from mass to weight.
Actual force probe reading: T ___________N
Actual Scale reading: n_____________N
What is the percent difference if you compare the calculated tension value from to the force probe
reading? Use the calculated value in the denominator.
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