Physics 152 – Lab 10: Equilibrium
Professor van der Veen
Lab instructors: Mr. Stankovich, Ms. Walker
Static Equilibrium
In this investigation you will explore the meaning of balancing all the torques and forces on a system, so
that it remains in equilibrium. You will use the principle of the mobile to create some very simple physics
lab art.
Equipment:
•
A meter stick, let’s call its mass M. We’ll assume that it is homogeneous (which, as you will
observe, it probably is not).
•
Three little clamps, each with mass around 17 grams, let’s call them mi.
•
Various small masses, in increments of 10 grams, that you’ll hang on the right and left sides,
adding their mass to the little clamps.
Procedure:
1. Find the mass of the meter stick. M =
2. Find the masses of the little clamps. m1 =
m2 =
m3 =
3. Clamp one of the little clamps at the 50-cm mark with the hook UP. Adjust the position of the
center clamp until the meter stick balances when you hang it by the hook. This is the center of
mass (CM) of the meter stick + central clamp.
Record the position of the CM of the meter stick with the clamp:
4. Measure the distance on each side of the balance point which is half way between the balance
point and the outer edge of the meter stick. On the right side, call this xR and on the left side, call
this xL. If the meter stick were perfectly homogeneous, its CM would be exactly at the 50-cm
Week of March 30, 2009
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Physics 152 – Lab 10: Equilibrium
Professor van der Veen
Lab instructors: Mr. Stankovich, Ms. Walker
mark, and the CM of either side would be +/- 25 cm from the balance point, but the meter stick is
probably not perfectly homogeneous, so the measurements will be a little off. This measurement
is important because the weight of each side of the meter stick, taken at the cm of each side, times
the distance from the balance point (CM) to the cm of each side, causes a torque on each side.
Balancing the meter stick means balancing the torques on either side.
xR= distance from balance point to cm of right side =
xL = distance from balance point to cm of left side =
Mass of each side: Ideally, the mass of each side is M/2. If the balance point is way off the 50-cm
mark, then the mass of each side is (M/L)x length of each side, measured from the CM. If it is close
enough, just call the mass of each side M/2.
5. Calculate the positive torque due to the mass of the left half of the meter stick as xR(M/2)g (or
whatever you got for the mass on the left side, if it is not half the total mass).
6. Calculate the negative torque due to the mass of the right half of the meter stick as xL(M/2)g
τ+ = x
L
τ- = x
(M/2)g =
R
(M/2)g =
These will be present in all your calculations when you try to balance the torques.
7. Now clamp each of the other little clamps to the edges of the meter stick. Be sure to screw the
clamps down with the hooks DOWN, as we will hang little masses off these hooks. Don’t move
the central balance point, but adjust the position of the clamps until the system is in equilibrium.
DEFINE:
RLeft = distance from balance point (CM) to mass on left. mL= mass of clamp on left side +
mass you hang on the left side
RRight = distance from balance point (CM) to mass on right. mR = mass of clamp on right side
+ mass you hang on right side.
+
With masses attached, the counter clockwise (positive) torque is τ = xL (M/2)g + RLeftmLg
and the clockwise (negative) torque is
= xR (M/2)g + RRightmRg
τ
8. Calculate the sum of all the torques. The torque on the left should equal that on the right.
9. Add 10 grams (.01 kg) to each side so that the meter stick is again in equilibrium. Again,
calculate the sum of all the torques.
10. Now add 10 grams to the mass on the left, and adjust its position so that the system is again in
equilibrium. Again calculate all the torques.
11. Repeat step 10 – add another 10 grams, and adjust the position until you get the system to balance
again in equilibrium. Again calculate all the torques.
Week of March 30, 2009
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Physics 152 – Lab 10: Equilibrium
Professor van der Veen
Lab instructors: Mr. Stankovich, Ms. Walker
12. Repeat step 11: Add another 10 grams on the left, and adjust the position of the left mass again
until the system is in rotational equilibrium. Calculate all the torgues for this new arrangement.
13. Keep repeating…What is the largest mass you can add on the left, and still get the system to
balance in equilibrium?
Data Table : Record the masses and distances from the balance point for each trial, and compute
the torque on each side.
What happens to the moment arm on the left side as you add more mass to the left side?
Part 2: Making torque-art!
For this part, get together with another group. Remove the extra masses from your meter stick,
and hang one meter stick from the other. Adjust them so that they are balanced, one above the
other. Now be as creative as you like: add mass to the upper stick, to the lower one, using a
combination of known masses and unknowns (such as keys, etc). Add at least four objects. When
you are satisfied with your mobile, DRAW a diagram of it in the space below, and analyze all the
forces and torques on it!
Week of March 30, 2009
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