Experiment 10: Equilibrium
Part 1:
You will see if the total torque on a stationary object is zero. Three scales, calibrated in
newtons, are hooked to a wooden block. They are put under tension to create forces on the
block. Reading the scales gives the magnitudes of the forces; tracing the scales on a sheet of
paper records their lines of action. Moment arms from one corner of the block are measured
on the tracing, and the torque from each force calculated. The total is then compared to
zero.
Procedure: With spring scales, apply three different forces of at least 5 N to the wooden
block. Slide a sheet of paper under the block. Trace the block and the scales. Record the
magnitude of each force on the paper, estimating to the nearest tenth of a newton. Each
person in your group should take their own data. However, there is no need to rearrange the
apparatus for each person.
Take the paper off the apparatus. Draw the line of action of each
force down the center of the scales, and all the way across the
paper, including arrowheads to indicate the direction. (The three
lines of action must meet at one point.) Label one corner of the
block as point P. Draw each force’s moment arm, the
perpendicular distance from P to its the line of action. (You can
use the corner of the ruler to draw a 90 angle.) Measure each
moment arm in centimeters and record it on the diagram. The
uncertainty in your data is .5 N for the spring scales, and your
own estimate for the ruler.
Under Calculations, find the torque of each of the three forces about the axis at P, and their
uncertainties. Recall that when multiplying numbers, you add percents of uncertainty.
Include step-by-step calculations in the space provided. To decide whether a torque is
positive or negative, it might help to press down on point P with your pencil point so that
you can actually rotate the sheet about that point. Then, notice which way the sheet turns
when you push along the line of action in the direction of the force.
Find the total torque and its uncertainty. Recall that when adding numbers, you add the
uncertainties themselves, not percents. Is the total torque about P equal to zero, within
experimental uncertainty?
Part 2:
You will calculate the string tension, S, in the model crane
shown, and see if it matches the reading on the scale along the
string. You will also calculate the force, H, from the hinge at
the lower end, but won’t check it experimentally. The crane
is made from a half-meter stick mounted on a ring stand as
shown. You will measure the weights and dimensions of the apparatus, then calculate the
string tension, S, using the second condition of equilibrium.
Data.
To save time, instead of calculating uncertainties, just wait until the end, and then assume
that computed value of S is good to + 5%, and the uncertainty in the measured value is .5 N.
Remove the boom from the crane and hang it from the spring scale to measure its weight,
including the metal clips. Calculate the weight of the load you will hang from it from the
mass, which should be at least 300 grams.
Locate the boom's center of gravity (including the clips) by seeing where it balances on your
finger. Remember where it is so you can find it later.
Reassemble the crane: Set its lower end in place. Then, hook the loop of string to the
newton scale, pass it over the pegs near the top of the boom, and hang the load from the
other end. You might want to wind the string around the pegs so it can't slip. Be sure the
string is horizontal, as shown.
Measure the moment arms. This is just like part one: For each force, measure the distance
from the hinge to the force's line of action along a perpendicular. (Calculating from the
length along the boom and an angle is the hard way.) For WB and WL, you might want to
use a string with a weight on the end to help you judge where the line of action is. Show
each moment arm on the picture on the data sheet, including arrows to show from where to
where you measured.
Calculations:
Use Στ = 0 to solve for the string tension, S. Note that S is the unknown you're solving for;
do not fill in the measured value. Show all steps of the calculation in the space provided.
Use ΣFx = 0 to find Hx, the x component of the force from the hinge. Similarly, use ΣFy = 0
to find Hy.
Now, read the spring scale to obtain the measured value of S. Does the computed value
agree with this measured value?
Experiment 10: Equilibrium
PART ONE:
(Attach sheet that you slid under block.)
Calculations:
τ1 =
τ2 =
τ3 =
Total torque =
PART TWO:
Boom Weight = ________________
Load Mass = __________________
Load Weight = ________________
On the diagram, use arrows to show
from where to where you measured
each moment arm.
Calculations:
Στ = 0
ΣFx = 0
ΣFy = 0
Measured value of S = ______________________