PHY 131/221
Force Table (Vector Addition)
(revised 4/26/08 J)
Name:_____________________
Date:________
Lab Partners:_____________________________________________
Introduction: Vectors are central to modeling forces and their effect on the motion of
objects. Using force tables you will be able to add vectors “experimentally”. Then you
will add those same vectors graphically and using the component method as discussed in
class. Do the results convince you that the component and graphical method accurately
represent the addition of forces in nature?
You have already encountered displacement and velocity vectors. What is a force
vector? First of all what is a force? If you need a pen from a drawer in your desk you
pull on the drawer to open it. To close your car door you push it until it closes. A basic
definition of a force is a push or a pull. Force is also a vector, it has a magnitude and a
direction. You are helping your friend rearrange the furniture in their living room. Your
friend asks you to put the table in the corner. You start to push the table when you realize
he didn’t say which corner. When you ask which corner he points. By pointing he has
made your motion of pushing the table a vector. You apply a force in a specific
direction.
Force in this class is measured in Newtons [N]. A Newton is a [kg · m/s2]. In this lab we
will be looking at the force of gravity on a mass hanger and masses. The force of gravity
will be calculated as,
Fg = mg
Watch your significant figures!
As you will see in the lab we will be using pulleys to redirect the vertical Force of gravity
(gravity always pulls toward the ground) in a horizontal direction.
I. Experimental Vector Addition
1) In each part of the lab you will have 2 to 3 force vectors to add together.
The magnitude of each force vector will depend the mass of the mass hanger and
masses placed on it. If you need a mass of 200g take a 50g mass hanger and add
150g in mass disks to get 200g. Then measure them together on a mass balance
to the correct number of significant figures. The labels on the masses are not
usually accurate!
2) To calculate the magnitude of the force vector multiply the mass by g = 9.80m/s2
1
3) Place each pulley at the angle indicated in the Data Table. For example, for Part 1
place a pulley at 60° and 120°. Then take your ring with the strings attached and
place it at the center of the table with the pin coming through the ring. Place a
string over each pulley and hang the appropriate mass hanger from each string.
Now you have your force vectors (magnitude mg and direction determined by the
location of the pulley).
4) Now to find the resultant vector. Pull on the remaining string in different angles
until you find an angle where the pin is directly in the center of the ring. Place a
pulley at this angle and hang an empty mass at this angle from a string. Place
additional masses on the hanger until the pin is at the center of the ring.
You now have a system in equilibrium. The last hanger is called the equilibrant
because it balances the system.
5) The resultant vector has the same magnitude as the Equilibrant, but points in the
opposite direction. The Resultant angle will be θR = |180° - θEquilibrant|.
To find the magnitude of the Resultant measure the equilibrant mass and multiply
by g.
II. Component Method
6) Take the force vectors in each part of the lab and calculate the resultant vector
using the component method. How do your results compare with the results from
the experimental addition?
III. Graphical Method
7) Choose an appropriate scale (eg. 1mm = 1N, 1 cm = 1 N, ?), then add the vectors
graphically in each part of the lab. How do your results compare with those from
the experimental and component method?
2
Data Table
Experimental
Results
Component
Method
Graphical
Method
→
→
→
→
m1 = ________
(200g)
F1 = ________ @ 60°
FR = ________
FR = ________
FR = ________
→
@ ________
@ ________
@ ________
m2 = ________
(200g)
F2 = ________ @ 120°
→
→
→
→
m1 = ________
(250g)
F1 = ________ @ 120°
FR = ________
FR = ________
FR = ________
→
@ ________
@ ________
@ ________
→
→
→
→
m1 = ________
(150g)
F1 = ________ @ 0°
FR = ________
FR = ________
FR = ________
→
@ ________
@ ________
@ ________
m2 = ________
(200g)
F2 = ________ @ 90°
m1 = ________
(150g)
F1 = ________ @ 50°
→
→
→
FR = ________
FR = ________
FR = ________
m2 = ________
(200g)
F2 = ________@ 90°
@ ________
@ ________
@ ________
Part 1
Part 2
m2 = ________
(200g)
Part 3
F2 = ________ @ 200°
→
→
Part 4
→
m3 = ________
(250g)
F3 = ________ @ 140°
3
Questions:
1.
Consider the three methods used to find the resultant vector, which method is the
most accurate? Explain.
2.
Give some possible sources of error for each method.
3.
Will the magnitude of FR be the same in Part 1 if we subtract the two vectors, F1 – F2,
instead of add them? Explain.
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4.
In this experiment you used the table in a horizontal position. How would your
results be different, if at all, were the table positioned vertically? Explain and justify your
answers with an example including calculations.
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