i need introducion and purpose, discussion and conclusion. and all the question. if you know a software to make the graph
7, February 2022
Force Table
By: Jackson Widener
Thomas
Jeremy
Sixto
Eric
Introduction & Purpose:
Diagram:
Data:
Experimental Procedure
|
Procedure |
F1 |
F2 |
F3 |
Equilibrant |
Resultant |
||||||||
|
Magnitude |
Direction |
||||||||||||
|
1 |
100 |
200 |
XXX |
222 |
244.5 |
||||||||
|
2 |
150 |
300 |
256 |
290` |
|||||||||
|
3 |
411 |
253.5 |
Graphical Procedure
|
F1 |
|||||||||
|
100 |
200 |
XXXXXXXX |
|||||||
| 150 | 300 | ||||||||
Analytical Procedure
|
223.607 |
63.43 |
|
259.808 |
110.011 |
|
409.267 |
72.216 |
Error Calculations
|
Error (Experimental) Magnitude |
Error (Experimental) Direction |
|
Error (Scale Drawing)Magnitude |
Error (Scale Drawing) Direction |
Discussion / Conclusion:
Questions:
1. Determine the magnitude and direction for the resultant and equilibrant for procedure 2.
2. Determine the magnitude and direction for the resultant and equilibrant for procedure 4.
3. Determine the magnitude and direction for the resultant and equilibrant for procedure 5.
4. Considering the results of the Analytical Procedure to be correct, calculate the percent error for the magnitude of the resultant for procedures 2, 4, and 5 for the experimental method.
5. Repeat calculation 4 for the results of the component procedures 7 and 8.
6. Report the magnitude and direction of the resultant for machine from procedure 2 and the analytical magnitude and direction from procedure two. Assuming the calculated value to be correct, report the percent error for the magnitude and direction.
Experiment
6
Vectors
Vectors
VECTORS: EQUILIBRIUM OF A PARTICLE
First Condition of Equilibrium
Physical quantities are divided into two broad general categories called scalars and vectors. Scalars are physical quantities that have size or magnitude only. Examples of such quantities are mass, volume, and time. A vector quantity is one that possesses both magnitude and a spacial direction. Vectors also obey the Commutative Law of Addition. Examples of vectors include force, velocity, and acceleration. Vectors are represented a line segment whose length is made proportional to the magnitude of the vector and the line segment is drawn in such a way as to point in the direction the vector is acting. The line representing the vector has an arrow on one end to indicate the direction the vector is acting.
A particle is an idealized point mass. That is, a particle behaves as if all parts of the mass making up the body have been confined to a single point. When a series or combination of forces acts on a particle, they may be replaced by a single force whose combined effect is the same as the combination of all forces. Under this condition, all the forces acting on the mass must pass through this point. The first condition of equilibrum states that the vector sum of all forces acting on a point is zero. The purpose of this exercise is to investigate various methods of testing the first condition including graphical, analytical and direct measurement.
In the graphical technique, a convenient scale factor is used to represent the magnitude of the force. For example, 1 cm on length could be used to represent a 5 N force.
When two or more forces acts on a point, the resultant is a single force which produces the same overall effect. The operation of adding vectors graphically consists of constructing a diagram in which a straight line is drawn from the origin of the first vector position and extending it in the direction the vector acts until its length is the same as magnitude of the vector. From the arrowhead of this vector and at the correct angle with respect to the first vector, another line representing the second vector is constructed. This process is continued until all vectors have been added.
The resultant of two or more vector is the displacement between the tail of the first vector and the head of the last vector. The direction the resultant points relative to the positive x-axis is the direction the resultant vector acts. The equilibrant is the single vector that will force a system of forces into equilibrium. It is equal in magnitude and opposite in direction to resultant. However, if all forces are in equilibrium, the forces will add to form a closed polygon.
In the Analytical method for vector addition, two techniques, the triangle method and the component method, are used. In the triangle method, the magnitude R of two vectors A and B is found by using the law of cosines if the angle opposite R is known.
Law of Cosines:
Where cos(A,B) is the cosine of the angle between sides A and B.
The angle between the resultant and side A can be found using the law of sines.
c
sin
C
b
sin
B
a
sin
A
=
=
In the Component method, the tail of all vectors is located at the origin of an x-y coordinate system with the magnitudes and directions accurately represented. A perpendicular is then dropped from the tip of each vector to the x-axis. Using the right angle function for sine and cosine of the angles made by the vectors with the positive x- axis, an x and y component of each vector is found. At this point, all the y-components of each vector can be added or subtracted since they act in the same or opposite directions. The same would also hold for the x-components.
After these steps have been followed, two vectors will remain which are perpendicular. The Pythagorean theorem can find the resultant of these final two vectors, and the direction of the resultant can be found by the tangent function.
In the Experimental method, a force table, a piece of apparatus that allows forces to be attached to a common point, is employed. The rim of the force table consists of a divided circle calibrated in degrees. Low friction pulleys with a pointer attached are connected to the rim. Weights are applied to the central ring by passing a string tied to the ring across the pulleys and continuing over the edge of the rim and attached to weight hangers. Weights are added to the pulleys and the position of the pulleys is adjusted along the divided circle until balance has been reached.
Apparatus:
1. Force table
2. Four pulleys
3. Four weight hangers
4. Set of slotted weights
5. Protractor
6. Metric
7. Ruler
)
,
cos(
2
2
2
2
B
A
AB
B
A
R
–
+
=
Procedure:
NOTE- As an aid to keep the size of numbers appropriate, the instructions will be to use the units of grams throughout. It must be noted that the gram is a unit of mass, not weight or force. However, weight is the product of mass and the acceleration due to gravity, g. Therefore, since g is the same on all masses, the gram (being proportional to force) an expedient unit.
Case I
Experimental Method
1. Assemble the force table apparatus according to the diagram. The table should be level and the strings attached to the center ring should point directly into the central pin.
2. Attach a string to the ring and pass it over a pulley attached to the 0° mark. Add a total of
F1 = 100 g to the weight hanger (including the weight of the hanger). Mount a second pulley at the 90° mark and add a total of F2 = 200 grams on this weight hanger.
3. Attach a third pulley to the table with enough weight attached to bring the entire system to equilibrium. This position is found by adding weights and adjusting angles so the ring just centers on the central pin. Since a little friction exists in the pulleys, you can lift the ring upward about 1 cm, release it, and let it vibrate up and down and see if it settles with the pin in the middle. Make whatever adjustments in this third force until you are satisfied that equilibrium has been established, then record the value. This third force is the equilibrant, which is equal and opposite of the resultant.
Case II
4. Mount a total of F1 = 150 g over a pulley attached to the 20° mark. Attach a total F2 = 300 g over a second pulley attached to the 140° degree mark. Repeat procedure 3 for this arrangement.
Case III
5. Mount three pulleys on the table, one at the 0° mark with at total of F1 = 200 g, one at the 60° mark with F2 = 150 g, and one at the 120° mark with F3 = 300 g.
6. Repeat procedure 3 for this arrangement.
Graphical Method
7. Using the circular graph provided for this experiment, construct a diagram drawn to scale from the data used in procedure 2. Use a convenient scale factor such that the entire sheet will be encompassed. Using the technique described in the Component Method, determine the magnitude and direction of the vector sum. Record this value.
8. Repeat procedure 7 for the cases described in procedures 4 and 5.
Analytical Method
9. Using the method described in the Analytical Method, determine the magnitude and direction of the resultant using the data in procedure 2. Record this value.
10. Repeat procedure 9 for the cases described in procedures 4 and 5.
Data:
Experimental Procedure
Procedure
F1
F2
F3
Equilibrant
Resultant
Magnitude
Direction
Magnitude
Direction
1
100
200
XXX
2
150
300
XXX
3
200
150
300
Graphical Procedure
Procedure
F1
F2
F3
Magnitude
Direction
1
XXXXXXXX
2
XXXXXXXX
3
Analytical Procedure
Procedure
F1
F2
F3
Magnitude
Direction
1
XXXXXXXX
2
XXXXXXXX
3
Error Calculations
Procedure
Error (Experimental) Magnitude
Error (Experimental) Direction
Procedure
Error (Scale Drawing)Magnitude
Error (Scale Drawing) Direction
Calculations:
1. Determine the magnitude and direction for the resultant and equilibrant for procedure 2.
2. Determine the magnitude and direction for the resultant and equilibrant for procedure 4.
3. Determine the magnitude and direction for the resultant and equilibrant for procedure 5.
4. Considering the results of the Analytical Procedure to be correct, calculate the percent error for the magnitude of the resultant for procedures 2, 4, and 5 for the experimental method.
5. Repeat calculation 4 for the results of the component procedures 7 and 8.
6. Report the magnitude and direction of the resultant for machine from procedure 2 and the analytical magnitude and direction from procedure two. Assuming the calculated value to be correct, report the percent error for the magnitude and direction.
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Physics with Computers
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