Notebook FV2 - Forces and vectors
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Iowa State University *
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Apr 3, 2024
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Lab FV2 - Forces and vectors
Equipment
Metal board with magnetic accessories:
o
Two pulleys
o
Force wheel with central floating disk
Set of hangers and masses
Important (READ!!!)
To lift and move the magnetic
components on the board, always handle
the component by the magnetic base.
Magnetic elements that are not in use
should be kept stuck to the back of the
board
Lab FV2 - Page 1
The apparatus
The apparatus illustrated below will be used to study the relation between forces in an equilibrium condition. Find the force wheel with the floating disk in the center. Three strings should be already threaded through the center hole. If one or more are missing, please ask your instructor for assistance.
Each of the strings should be used to support a hanger with masses as shown. The pulleys have very low friction, so the tension in the strings will be equal to the weight of the hanger + masses.
Do NOT use the same masses left and right
(
i.e
., do not use a symmetrical setting: it’s a boring one!). Start by placing mass on the center hanger, then add masses to the other hangers and adjust the angles of the strings by moving the pulleys until the disk at the center of the force wheel is more or less “floating”. Finally, lift the force wheel gently off the board and move it on the board as needed until the floating disk is perfectly centered with the force wheel. In this position, the disk is, indeed, floating: it is not in contact with the wheel. If we neglect the weight of the disk (which is indeed very small), the only forces acting on it are the three tensions in the strings. Lab FV2 - Page 2
Prelab review: components of forces and propagation of uncertainty
For this activity, we will concentrate on one of the forces: the tension in the top, right string, indicated as T
1
in the figure below.
What is the magnitude of T
1
in your setup? Don’t forget to take into account the mass of the blue hanger!
56 degrees
22 grams
22 * 9.81 = 215.82 millinewtons
Forces are vectors, and so we need to work with their components. Write the components of T
1 for the coordinate axes shown in the figure, in terms of the magnitude T
1
and the angle θ
1
. (This should be an algebraic expression, do not use numerical values yet.)
T
1
x
=
T
1
cosϴ
T
1
y
=
T
1
sinϴ
To measure the angle with ease, the dial of the force wheel can be rotated to align the 0° mark with +
x
direction. If your x axis is horizontal, the bubble level will be helpful.
What is the value of θ
1
in your setup? ϴ
1
=
56
degrees
Lab FV2 - Page 3
Use the measured value of T
1
and θ
1
to calculate the numerical value of the components of .
T
1
x
=
120.68
millinewtons
T
1
y
=
178.92
millinewtons
Uncertainty
However, no measurement is perfect! The masses we are using have an uncertainty of
2% around their nominal value.
A reasonable estimation of the uncertainty in the angles could be set to
1° (we can read the angle with
a precision of about 0.5°, but we are increasing it to account for the friction in the system, which results in a certain variation in the position of the strings in equilibrium).
Rewrite the values of your experimental values for T
1
and θ
1
, including uncertainty:
T
1
=
(
215.85
±
4.32
)
millinewtons
ϴ
1
=
56
±
1
Uncertainty is propagated through any calculation. Rewrite the components of including uncertainty. (This is what you did in the prelab.)
T
1
x
=
120.68
±
4.75
millinewtons
T
1
y
=
178.92
±
3.21
millinewtons
Lab FV2 - Page 4
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