PROJECTILE MOTION
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FORCES IN EQUILIBRIUM
GOAL
To study the characteristics of force and the conditions that bring about equilibrium of a rigid body
acted upon by several forces.
PREREQUISITES
R.D. Knight, College Physics, Chapters 4, 5
EQUIPMENT
Force Table
Weights
THEORY
Force is one of the most fundamental concepts in mechanics. A force is an action of one object on
another object which changes or tends to change the state of motion of the object acted on.
In this particular work you have to deal with static equilibrium. Static equilibrium requires that the net
force (the sum of the forces acting on object) is zero:
.
Note that we have to sum up vectors not scalars. A vector has both magnitude and direction to be considered
together.
To find the sum of a few vectors you can use two different methods:
· Graphical or tail-to-tip method
· Algebraic method based on the coordinate representation of the vectors
The second method is more general and ensures better accuracy then the first one. To add vectors by
components you have
1. to resolve each vector into its components (to find coordinate components of each vector)
2. to sum up the relevant coordinate components
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PROJECTILE MOTION
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Finally you can return to standard vector representation using equations
PROCEDURE
In the Force Table, the forces are provided by gravity acting upon weights and weight
holders. The direction of the force vectors is determined by pulleys arranged around an angle scale. Thus
both quantities of the force vectors, the magnitude and direction, can be determined.
· Set the Force Table on a supporting table.
· Level the Force Table with the adjusting screws on its feet. This adjustment is not critical
but the hanging weights should hang vertically.
· Place the ring over the central post. This will keep everything in place while making
adjustments.
· Attach three of the weights holders and hang them over three of the edge pulleys at angles
specified by your instructor.
· Distribute three weights, specified by your instructor, over three attached weight holders.
· Calculate the magnitude (forth weight) and position (angle) of the force which equilibrate
the three given forces.
· Attached fourth weight holders at appropriate position.
· When nearly balanced, lift the center ring a little and drop it to vibrate the system a little to
overcome friction. Make sure that the pulleys are adjusted so that the string passes directly
over the index line on the pulley. This will assure that the string is passing straight over the
pulley to the center of the table.
· Have your instructor verify your setup.
· Tabulate the angles and weights in the table. Note that all numbers in table are given just
for illustration.
N of
weight
1
2
3
Weight(kg)
Force(N)
0.2
0.5
0.04
1.96±
4.9±
0.398±
Angle(degree)
X component
Y component
1.70±
-1.68±
-0.07±
-0.05±
0.05±
0.00±
0.98±
4.60±
-0.39±
5.19±
-5.19±
0.00±
30º
110º
260º
Totals of three:
4
·
Totals of four:
Repeat the work for another set of weights and angles.
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ANALYSIS AND LAB REPORT
1.
2.
3.
4.
5.
6.
Write your name and list names of all your partners.
Write the date of experiment.
Write the title, goal, and list of equipment of the experiment.
Supply the table with your results.
Give your calculations of the equilibrating force.
Examine the possible sources of errors in experiment and calculations. Identify where the
largest errors come from. Write a small (a few statements) essay.
7. Why calculated force (equilibrating force) does not equilibrate three given forces perfectly.
Write a small (a few statements) essay.
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