University of Evansville Physics Torques and Center of Gravity Lab Report Hello, due to the COVED-19 Crisis. I have gotten a little behind on my Physics la

University of Evansville Physics Torques and Center of Gravity Lab Report Hello, due to the COVED-19 Crisis. I have gotten a little behind on my Physics lab, Therefore, I need help finishing up this Physics lab: Torques and CG

I’ve attached a data spreadsheet. I’ve also attached a copy of the experiment, I suggest you start this experiment by watching the four videos on You Tube that explain it.

https://www.youtube.com/channel/UCScoMECtlulz_dFWnEw7Okw

The videos for this experiment are Torques 1, Torques 2, Torques 3, and Torques 4. Watch them in that order. Then after watching those, start reading the experiment in the manual and doing it, as though you were doing it in the lab. You may find it helpful to go back and re-watch some of the videos as you progress through the experiment.

You’ll find measurements you need in the Torques Data spreadsheet. In the same spreadsheet, you can record results of your calculations. Every cell that’s yellow will require you to enter a value. Always record units in the next column to the right. Here and there in the spreadsheet, I also throw in some bits of guidance.

It’s possible in some places you might find it helpful to change the formatting for a cell. You might need to change the number of decimal places displayed in that cell in order to properly display your value. If you show a couple more significant figures than you properly should have, we will overlook that. But you don’t want to show too few. If you find you can make things more clear by adding a row or column here or there, that’s fine.

The lab manual uses Greek letter tau for torques. But in the spreadsheet we use T instead.

Thanks In advance,

Please let me know if you have any further questions Torques and Center of Gravity (p. 93)
Name:
The given measurement values are in the cgs system of units.
Convert to SI when you calulate.
Part I, p.93:
mclamp=
xF=
21.2 g
49.5 cm
M=
83.2 g
2)
To get masses m1 and m2, you’ll have to add:
Hanging at location 1 are the clamp, the mass hanger (50g), and a 100g disc.
Hanging at location 2 are the clamp, the mass hanger (50g), two 20g discs, and one 5g d
x 1=
m1 =
20.0 cm
r1=
w1=
x 2=
r2=
91.8 cm
m2 =
w2=
3)
T1=
T2=
Ttot=
Tip: You expect Ttot to be small, right? Ideally it would be zero.
But what constitutes “small” depends on the scale of numbers you’re working with at th
Learn to see it in relative terms.
Think about the size of Ttot as a percentage or fraction of T1 or T2.
Part II:
1)
W=
2)
This is the weight of the meter stick
For the rest of the experiment, I’ll just give you total mass hanging at a location on the m
xA=
10.0 cm
mA=
83.2 g
FA=
rCG=
computed xCG=
observed xF=
(This is just re-entering the x F measured at the beginning of the experiment.)
0.2
Part III, p.97:
2)
x C=
40.0 cm
xA=
rA=
mA=
FA=
20.0 cm
226.2 g
x B=
rB=
mB=
FB=
80.0 cm
93.2 g
3) Ttot (C) =
List the individual torque values below that you add up to get the total:
(If you want to, you could show how you calculated them too.)
4)
FC= 3.9452
Notice: this question is asking for force , not torque.
List the individual force values below that you add up to get the total:
5) Ttot (0) =
List the individual torque values below that you add up to get the total:
(If you want to, you could show how you calculated them too.)
Part IV:
1)
2)
Name __________________________________________ Lab Section_____________________
Partner ________________________________________ Date __________________________
TORQUES AND CENTER OF GRAVITY
OBJECT: By calculating the torques produced by vertical forces acting on a meter stick mounted
on a pivot, the student will (a) verify that the algebraic sum of the torques acting on any object in
equilibrium is zero; (b) locate the center of gravity of the object by computing the line of action of
the equivalent gravitational force; and (c) compare torques with different points chosen as the axis.
APPARATUS: meter stick, stand, lab jack, 3 knife-edge clamps (2 with wire loops), mass hangers,
slotted masses, triple-beam balance
BACKGROUND: Consider a force F, acting on an object at a certain point (known as the “point of
application.”) The position of the point of application, relative to an arbitrarily chosen point O
(known as the “axis”) is given by the vector r. The torque produced by the force F, about the axis O,
is defined as
?=r× F
(? is a vector that is perpendicular to both r and F, with magnitude ? = r F sin?.)
In today’s experiment, all the forces act vertically (up or down), and all the distances r will be
measured along the length of a horizontal meter stick, so ? = 90°, so
? = ± rF
Since all our torques then point along the same line, we can add them as (positive or negative) scalar
quantities. We will adopt the usual convention of treating counterclockwise (CCW) torques as
positive and clockwise (CW) torques as negative.
PROCEDURE:
Part I: Two Opposing Torques
Record the average of the masses of the two clamps. Record the mass M of the meter stick.
mclamp = _______________________
M = _______________________
1)
Attach the knife-edge clamp (the one without a wire loop) to the meter stick near the 50 cm
mark. Carefully adjust the position of the clamp so the meter stick balances in a horizontal position.
Record the location of the fulcrum (which in this case is the center of gravity of the meter stick,
though in general the fulcrum can be placed anywhere):
2)
xF=_______________________________.
Now attach a wire-loop clamp to the meter stick near the 20 cm mark, and hang an additional
93
150 g (including the mass of the hanger) from this clamp. (Value of m1 will be
approximately 170 g.) Record the actual position, mass, and weight:
Throughout this experiment, “mass” will refer to the total mass of the weight hanger,
slotted weights, and the clamp from which it hangs. The position of a mass hanger as
read directly from the meter stick will be x, but the distance of the hanger from the axis
of rotation will be r.
x1=_______________________________
m1=_______________________________
r1=_______________________________
w1=_______________________________
Now attach a second clamp to the meter stick and hang 100 g (including the mass of the
hanger) from this clamp. Adjust the position of this clamp to balance the meter stick.
Record the actual position, mass, and weight:
3)
x2=_______________________________
m2=_______________________________
r2=_______________________________
w2=_______________________________
Compute the two torques acting on the meter stick, using the fulcrum as the axis.
?1=__________________________
?2=__________________________
4)
What is the total (algebraic sum) of all the torques acting on the meter stick?
?tot=_________________________
Part II: Locating the Line of Action of the Gravitational Force
94
When the earth pulls down on the meter stick, it is pulling down on each of the large numbers of
protons, neutrons, and electrons that make up the meter stick with large numbers of tiny gravitational
forces, one on each particle:
We know the vector sum of all these individual forces. It is just the weight W of the meter stick!
W = w1 + w2 + w3 + …
1)
Determine the magnitude of the vector of the sum of the gravitational forces acting on the
bare meter stick (W):
W = ____________________________
Relative to any given axis, each of these gravitational forces will produce a gravitational torque, so
there will also be a total gravitational torque:
?grav = ?1 + ?2 + ?3 + …
If we wish to talk of a single effective gravitational force acting on the meter stick (its “weight”),
certainly this force must equal the total gravitational force. Less obvious, but equally important, is
the fact that the torque produced by this effective force must equal the total gravitational torque.
Since the torque produced by any given force depends on the force itself and its point of application,
we will define the center of gravity (CG) of an object as the point where W must act so that its torque
equals the actual gravitational torque:
?grav = W · rCG
2)
Attach the knife-edge clamp at point B, the 30 cm mark on the meter stick. Now attach a
wire-loop clamp near the 10 cm mark (I’ll call this point A) and hang enough weight to just
balance the meter stick. (You may need to adjust its position slightly to level the meter stick
95
precisely.)
Record the data below:
Final location of the wire-loop clamp: xA =_________________
mass at location A:______________________________
force applied at point A: FA = ______________________
If we compute the torques acting on the meter stick with the fulcrum chosen as the axis, we find that
the upward force of the support produces no torque. We have a counterclockwise torque due to the
weight at point A, and this torque must precisely cancel the total gravitational torque acting on the
entire meter stick:
?A + ?grav = 0
FA· rA ? W· rCG = 0
In this last equation, we know all three quantities except rCG, the distance from the axis (in this case,
the fulcrum) to the center of gravity, so we may compute rCG:
rCG =_________________________________
Finally, what is the position of the center of gravity, measured from the zero end of the meter stick?
(computed) xCG =_________________________
96
For comparison, refer to Part I, step 1) and record the experimentally observed location of the center
of gravity.
(observed) xF =_________________________
(Note that Part I interpreted the CG as the “balance point” of the meter stick, while Part II
emphasized the CG as the point where the weight of the meter stick acts. In fact, the two
interpretations are exactly equivalent.)
Part III: Changing the Axis
1)
Slide the knife-edge pivot to some point C on the meter stick (not the center of gravity!)
Then hang two different weights at point A and B, and adjust their masses and positions to
make the meter stick balance.
2) Record the data below:
location of point C: xC =___________________________
xA =___________________ xB =__________________
rA =___________________ rB =__________________
mA =__________________ mB =__________________
FA =__________________
3)
FB =__________________
Compute the total torque acting on the meter stick, using point C as the axis for each torque.
(For the weight of the meter stick, use the directly observed location from Part I, step1.)
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?tot(C) =__________________
4)
Calculate the upward force acting on the meter stick at point C:
FC =__________________
5)
Now compute the total torque acting on the meter stick with 0 cm chosen as the axis for each
torque. (Again, for the line of action of the meter stick’s weight use the observed location of
the center of gravity.)
?tot(0) =___________________
Name __________________________________________ Lab Section_____________________
Partner ________________________________________ Date __________________________
Part IV: Questions
98
1)
You are given a baseball bat, a knife edge (to use as a fulcrum), a 1.00 kg weight, a tape
measure and some string. Explain, using diagrams, words, and equations, how you could
determine the weight of the bat.
2)
You have perhaps noticed that the “500 gram” counterweight that can be hung from the outer
end of the beam on your balance is noticeably smaller than an actual 500 gram mass. A
simplified diagram of the balance is shown below. If a = 7.5 cm, and b = 24.5 cm, what is
the actual mass of the counterweight? (Neglect the weight of the beam itself.)
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100

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