Name:
Lab Partners:
Force Vectors
Purpose: To study force vectors in equilibrium.
Equipment: Force table, mass set w/hangers, 3 pulleys w/clamps
1) Attach the force table legs.
1st Setup
2) Attach a pulley w/clamp to the force table at each of the following angles: 0°, 90°, 210°.
3) There should be three strings at the top center of the force table. Separate these three strings and put
one string over each pulley.
4) Adjust the pulley heights so the string is close but not touching the top surface of the force table.
The strings should be approximately horizontal above the force table.
5) Attach a mass hanger to the loop at the end of each string, so the mass hanger hangs down over the
pulley.
6) Hang a total of 150 grams from the hanger at 210°. (Don’t forget to account for the mass of the
hanger as a part of the total.)
7) Use trial and error to determine the masses to hang over each of the other two pulleys, at 0° and 90°,
to exactly balance the mass at 210° (i.e., to achieve equilibrium), as follows:
• When the system is in equilibrium, the small clear disk that holds the three strings should be
centered over the string tie in the center of the force table.
• Pull the clear disk slightly to one side and let it go. The disk should return to the center. If not,
adjust the masses at 0° and 90° until the clear disk always returns to the center when pulled to
one side and let go.
8) Once equilibrium is established, record the masses at 0° and 90°. (Don’t forget to account for the
mass of the hanger as a part of the total.)
9) Just for this lab, we will “pretend” that forces are in units of grams. So, we will treat the force
magnitudes, F1 and F2 , as though they are equal to the masses, m1 and m2 , respectively. (This
avoids converting grams to kg, and then multiplying by g.) So, write here the experimentally found
magnitudes, F1 and F2 , in grams (same values you wrote for the previous question).
Force Vectors
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Now we will check to see if the theory gives the same results.
10) Draw a free-body diagram showing all
three forces (at 0°, 90°, and 210°) pulling
on the center clear disk.
11) Write each of the force components listed below in terms of their magnitudes, in symbols. The xcomponents are done for you as examples. (If any are equal to 0, just write that.)
x-components:
y-components
F1x = F1 cos0 = + F1
F1y =
F2 x = F2 cos90 = 0
F2 y =
F3 x = F3 cos 210 , OR − F3 cos30
F3 y =
12) Now, treat both magnitudes F1 and F2 as unknowns, to see if the theory can give us the same
results we found by experiment earlier.
In equilibrium, the sum of the force vectors (net force) on the clear disk is zero (in both x and y directions). I.e., F1 + F2 + F3 = 0 . Use this to find the magnitudes, F1 and F2 , both in terms of the
known magnitude F3 (in symbols). Write the x and y-component equations in symbols first! The xcomponent is done for you as an example. Show your work.
x-components:
y-components
F1x + F2 x + F3 x = 0
( + F1 ) + ( 0) + ( − F3 cos 30 ) = 0
F1 = F3 cos 30
13) Plug in the known value of F3 to calculate theoretical values for F1 and F2 , all in grams.
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14) Determine the percent errors in the experimentally measured values of F1 and F2 , compared to the
respective theoretical values you just found.
Percent error = 100*(difference between the two values)/(theoretical value)
2nd Setup
15) Move the pulleys so they are at 40°, 150° and 270°.
16) Hang 100 grams at 270°. This will be the known force magnitude, F3 (in grams).
17) Draw a free-body diagram showing all three
forces pulling on the center clear disk.
18) Write each of the force components listed
below in terms of their magnitudes, in
symbols. (Refer to the example shown with
the first setup, if needed.) Watch signs!
x-components:
y-components
F1x =
F1 y =
F2 x =
F2 y =
F3 x =
F3 y =
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Name:
19) Use the fact that the sum of the force vectors (net force) on the clear disk is zero (in both x and ydirections) to calculate the theoretical values of unknown magnitudes F1 and F2 . Write the x and ycomponent equations in symbols first! Show your calculations.
HINT: You should get two equations for two unknowns that you can then solve.
20) Try hanging these masses from the strings at 40° and 150°. Do you have equilibrium?
21) Try adding and subtracting 1 or 2 grams from each of these two hangers. Does this improve the
equilibrium?
22) Disassemble the force table legs and store them on the clips on the bottom of the table.
Force Vectors
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