Rotational Equilibrium Experiment (A discussion of rotational equilibrium princi
ID: 1443870 • Letter: R
Question
Rotational Equilibrium Experiment
(A discussion of rotational equilibrium principles follows the instructions.)
Purpose
This experiment is designed so the student can physically produce rotational equilibrium of a simple system and verify by calculation of torques that the system is balanced. The student will then use the principle of rotational equilibrium to determine the unknown mass of an object.
Equipment
180 US pennies dated 1983, or later.
10 US nickels. Note: nickels in a plastic bag make a better unknown than
the large nut shown in the video clip.
A weight or a large book
Meterstick or metric tape
36-inch long 5/16-inch diameter wooden dowel. [Any other uniform fairly
rigid stick will work fine too.]
4, 12-inch long pieces of string
3 small plastic bags, the lighter the better.
Procedure
The results of this experiment should be quite good, so be patient when balancing the beam. Read each location to the nearest millimeter. View the Torque video clip. The procedure followed in this clip is identical although the equipment is slightly different.
Part I: Finding the location of the balance point or fulcrum
Locate the center of the dowel and make a small mark there.
Tie a slip knot in one end of one of the pieces of string and slide the dowel
into the loop. Move the loop to the point you marked in the first step and
tighten.
Place the other end of the string over the edge of a table and place a
weight or book over the string to hold it and the dowel in place. In the diagram a 1.00-kg, brass mass has been used but anything heavy enough will work.
If necessary, slide the slip-knot one way or another until the balance point for the empty dowel is found. Once this point is found tighten the knot and make a small mark
on the dowel at either side of the string so you can find this point quickly if the knot should slip later. This dowel-support-string serves as the fulcrum and should remain at the same place throughout the rest of the experiment.
Part II: Equilibrium with two torques
Your weights are pennies in plastic bags.
Place 40 1983- or later- pennies in one plastic bag. The pennies,
plastic bag and one piece of string constitute mass 1. The total mass m1 is the sum of the 100 grams of pennies, the mass of the string and the mass of the plastic bag. A good approximation for the total mass of bag and string is 1.50 g. Record this mass 1, in kilogram units, in Table one. [Recall that 1 g = 0.001 kg so 100 g = 0.100 kg.]
Make up masses 2 and 3 in similar ways by placing 60 pennies in a second bag and 80 pennies in a third. Mass 2 is the bag with 60 pennies plus a string and plastic bag. Mass 3 is found in a similar way.
Record masses 2 and 3, in kilograms, in Table 1
Place mass 1 at a point 10 cm from the left end of the dowel. The
figure given above shows how to attach the masses not where to attach them. You’re going to have to be inventive or have three hands to do this. Now, you need the moment arm for mass 1. It is the distance from mass 1 to the balance point [fulcrum]. After balancing the dowel-weights combination you will measure this distance.
Place mass 2 on the right side of the dowel and move it to the right or left until the system [dowel plus two masses] is balanced [level]. This condition is indicated in the figure shown above.
Once you have the system balanced, carefully measure the distance from mass 1 [on the left] to the balance point and record as L1. Next measure the distance from the balance point to mass 2 and record as L2.
Calculate torque 1 and record it in Table 1. Torque 1 = m1gL1.
Calculate torque 2 and record it in Table 1. Torque 2= m2gL2.
Torques 1 and 2 should be very nearly the same. Calculate the
percent difference between them by using the following formula.
% difference = torque1 torque2 ×100 torque1+ torque2
Part III: Equilibrium with three torques
Part III is worked just like Part II except there are two masses on the left
side of the fulcrum and 1 on the right.
Place mass 2 somewhere between mass 1 and the balance point, and
put mass 1 at 10 cm from the left end, as in part II.
Place mass 3 on the right side of the dowel and move it until the
system is balanced. If you have to move mass 2 closer to the fulcrum to achieve a balance that is okay.
Determine the values of L1, L2, and L3 in the same manner as in part II of this experiment and record in Table 2.
Calculate the three torques and record in Table 2.
This time there are two, counter-clockwise torques and one clockwise
torque that balance. Add torques 1 and 2 and record the answer in Table 2. Now compare the sum of torques 1 and 2 with torque 3 by finding the percent difference using the same sort of equation as before.
Part IV: Finding an unknown mass
When you step on the type of scale used in most physicians offices the
nurse slides a weight on a beam to balance your weight. The markings on the beam tell her/him your weight. We will now use this same procedure to determine the unknown mass of an object.
To make your unknown place the 10 US nickels in a plastic bag.
Using one of the paperclips place the unknown on the right side of the
dowel at some location. The unknown mass is now mass 2.
Place mass 1 [40 pennies in a plastic bag] on the left side of the dowel.
Now move either mass 1 or mass 2 until the system balances.
Measure the distances from mass one to the balance point and record
as L1 and measure the distance from the unknown to the balance point and record as L2 in Table 3. Record mass 1 in the table and calculate and record torque 1 in Table 3. Calculate torque 2. Torque 2 will have an unknown mass in it. That is L2 is known and g is known but m2 isn’t. Suppose L2 were 0.20 m then torque 2 would calculated as m2gL2 = m2 * 9.8m/s/s*0.2 m = 1.96m2. Record the result of your calculation [not mine] in Table 3.
Set torque 2 equal to torque 1 and solve for the unknown mass. Record this in lower right-hand cell of Table 3. Since this is a true unknown you will not compute a percent difference.
Answer the questions and submit your report via the Assignments Drop Box.
Discussion of Rotational Equilibrium Principles
When an object is in rotational equilibrium, it is either not rotating or rotating at a constant rate. In this experiment only the first condition will be met. For an object to be not rotating the sum of the moments of force or torques must equal zero. Alternatively, this can be stated that the sum of the clockwise torques must equal the sum of the counter-clockwise torques.
A torque is the product of a force and a moment arm. The moment arm is defined as the perpendicular distance from the axis-of-rotation to the line-of- action of the force. For this experiment, the moment arm for each force is simply the distance from where the force acts on the dowel to the fulcrum.
Then, for a case with only two torques, the equation would be
torque =torque 12
FL=FL 11 22
m gL = m gL 1122
With this equation we can solve for either of the variables when the other three variables are known. This is the procedure you’ll use in part 3 of the experiment to determine the mass of the bag of nickels.
Exp. UNIT 8: Rotational Equilibrium Report
Two Unequal Masses Producing Equilibrium
Balance point in meters (X0)
Mass 1 in kg (m1)
Distance from Mass 1 to X0 in meters (r1)
Torque 1 in N-m [m1*g*r1]
Mass 2 in kg (m2)
Distance from X0 to Mass 2 in meters (r2)
Torque 2 in N-m [m2*g*r2]
Percent Difference in torques 1 and 2
Three Unequal Masses Producing Equilibrium
Balance point in meters (X0)
Mass 1 in kg (m1)
Distance from Mass 1 to X0 in meters (r1)
Torque 1 in N-m [m1*g*r1]
Mass 2 in kg (m2)
Distance from Mass 2 X0 to in meters (r2)
Torque 2 in N-m [m2*g*r2]
Torque 1 + Torque 2 in N-m
Mass 3 in kg (m2)
Distance from Mass 3 X0 to in meters (r2)
Torque 3 in N-m [m2*g*r2]
Percent Difference between sum of torques 1and 2 and torque 3
Known and Unknown Masses Producing Equilibrium
Balance point in meters (X0)
Distance from Mass 1 to X0 in meters (r1)
Torque 1 in N-m [m1*g*r1]
Mass 2 in kg (m2)
Distance from X0 to Mass 2 in meters (r2)
Torque 2 in N-m [m2*g*r2]
[m1*g*r1] = [m2*g*r2] (solve for m1 and write the number of kg in the cell.)----à This is the exp. value of the unknown.
Questions:
1. What are the major sources of experimental error?
2. Did we really have to multiply by g to find the unknown mass? Then why did we do so?
Two Unequal Masses Producing Equilibrium
Balance point in meters (X0)
Mass 1 in kg (m1)
Distance from Mass 1 to X0 in meters (r1)
Torque 1 in N-m [m1*g*r1]
Mass 2 in kg (m2)
Distance from X0 to Mass 2 in meters (r2)
Torque 2 in N-m [m2*g*r2]
Percent Difference in torques 1 and 2
Explanation / Answer
The real experiment needs to be performed to record the values asked in different tables.
The answers to the questions are provided below
1)Sources of error are
a) Since a proper weighing machine is not being used, so measured weights and hence masses may not be very accurate
b)Approximated value of string and plastic bag may no be very accurate.
2)No, multiplication by g was not necessary.
We do it merely to balance dimensions of physical quantities on both sides of an equation
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