211 Translational Equilib
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- Pages: 2
Title:
Translational Equilibrium/Vector Forces
Purpose:
The conditions necessary for the equilibrium of a set of concurrent forces is experimentally verified.
Apparatus:
Force table with pulleys, ring and strings attached, weight hangers, set of weights.
Procedure:
Various arrangements of forces are obtained by varying the magnitude and/or the angular positions of the forces on the force table. The magnitude is changed by changing the weight applied to the weight hanger, the angular position by moving the pulley to a different angle as indicated by the index marker. A.
B.
Mount a pulley on the 210° mark on the force table and suspend a total of 100 grams over it. Mount a second pulley on the 30° mark and suspend a total of 200 grams over it. Mount a third pulley at 90° with 150 grams over it. Experimentally find the magnitude and position of a fourth force required to achieve equilibrium. When equilibrium is attained the ring will be in the center of the force table and not touching the center pin. How far can the fourth pulley be moved to cause an obvious disruption from equilibrium? Keeping the position fixed slightly vary the magnitude of the equilibrium force. What is the sensitivity of the apparatus, i.e., how much deviation of the magnitude or the angle causes an obvious disruption from equilibrium? Repeat the procedure for a set of forces provided by the lab instructor.
Analysis: A.
Using the method of the resolution of forces calculate the resultant force for Procedure A. Then calculate the equilibrium force. Compare the calculated equilibrium force with the equilibrium force obtained experimentally.
B.
Repeat Analysis part A for the set of forces provided by the lab instructor.
1.
How could the sensitivity of this apparatus be improved?
2.
What effect would tilting the plane of the force table 30C have on your results? Explain.
3.
What do you think is the major cause for error in this experiment?
4.
Draw the force diagrams and the x - y force components (as shown in the theory section) for each of the given experimental set of forces. Also draw the equilibrium forces in your diagrams.
5.
What is the difference between a resultant force and an equilibrium force?
6.
Suppose you mounted the following set of weights on your force table: A = 100 grams at the 30 degree mark, B = 150 grams at the 135 degree mark, and C = 200 grams at the 270 degree mark. Calculate the fourth force (giving mass and angle) needed to achieve equilibrium.
Questions:
Translational Equilibrium / Vector Forces
page 1of 2
7.
Three forces of equal magnitudes are used to achieve equilibrium on a force table. What can you conclude about the angles between these forces?
8.
Three forces are in equilibrium on a force table. One has a magnitude a 10 N. The other two have equal magnitudes. What minimum magnitude could these two forces have? What maximum magnitude could these forces have? Explain.
Theory: Ay
A
+X
Ax
Cx
Bx
C
B
By
Cy
Resolution of vectors A, B, and C: Ax = A cos θΑ
Ay = A sin θΑ
Bx = B cos θΒ
By = B sin θΒ
Cx = C cos θC
Cy = C sin θC
Where all angles are measured counter clockwise from positive x axis. Magnitude of the resultant of the three vectors = (A x + B x + C x ) 2 + (A y + B y + C y ) 2 Angle of the resultant of the three vectors = A y + By + Cy arc tan A ( x + Bx + Cx ) The fourth vector required to achieve equilibrium is equal in magnitude and opposite in phase to the resultant of A, B, and C.
Translational Equilibrium / Vector Forces
page 2of 2
Translational Equilibrium/Vector Forces
Purpose:
The conditions necessary for the equilibrium of a set of concurrent forces is experimentally verified.
Apparatus:
Force table with pulleys, ring and strings attached, weight hangers, set of weights.
Procedure:
Various arrangements of forces are obtained by varying the magnitude and/or the angular positions of the forces on the force table. The magnitude is changed by changing the weight applied to the weight hanger, the angular position by moving the pulley to a different angle as indicated by the index marker. A.
B.
Mount a pulley on the 210° mark on the force table and suspend a total of 100 grams over it. Mount a second pulley on the 30° mark and suspend a total of 200 grams over it. Mount a third pulley at 90° with 150 grams over it. Experimentally find the magnitude and position of a fourth force required to achieve equilibrium. When equilibrium is attained the ring will be in the center of the force table and not touching the center pin. How far can the fourth pulley be moved to cause an obvious disruption from equilibrium? Keeping the position fixed slightly vary the magnitude of the equilibrium force. What is the sensitivity of the apparatus, i.e., how much deviation of the magnitude or the angle causes an obvious disruption from equilibrium? Repeat the procedure for a set of forces provided by the lab instructor.
Analysis: A.
Using the method of the resolution of forces calculate the resultant force for Procedure A. Then calculate the equilibrium force. Compare the calculated equilibrium force with the equilibrium force obtained experimentally.
B.
Repeat Analysis part A for the set of forces provided by the lab instructor.
1.
How could the sensitivity of this apparatus be improved?
2.
What effect would tilting the plane of the force table 30C have on your results? Explain.
3.
What do you think is the major cause for error in this experiment?
4.
Draw the force diagrams and the x - y force components (as shown in the theory section) for each of the given experimental set of forces. Also draw the equilibrium forces in your diagrams.
5.
What is the difference between a resultant force and an equilibrium force?
6.
Suppose you mounted the following set of weights on your force table: A = 100 grams at the 30 degree mark, B = 150 grams at the 135 degree mark, and C = 200 grams at the 270 degree mark. Calculate the fourth force (giving mass and angle) needed to achieve equilibrium.
Questions:
Translational Equilibrium / Vector Forces
page 1of 2
7.
Three forces of equal magnitudes are used to achieve equilibrium on a force table. What can you conclude about the angles between these forces?
8.
Three forces are in equilibrium on a force table. One has a magnitude a 10 N. The other two have equal magnitudes. What minimum magnitude could these two forces have? What maximum magnitude could these forces have? Explain.
Theory: Ay
A
+X
Ax
Cx
Bx
C
B
By
Cy
Resolution of vectors A, B, and C: Ax = A cos θΑ
Ay = A sin θΑ
Bx = B cos θΒ
By = B sin θΒ
Cx = C cos θC
Cy = C sin θC
Where all angles are measured counter clockwise from positive x axis. Magnitude of the resultant of the three vectors = (A x + B x + C x ) 2 + (A y + B y + C y ) 2 Angle of the resultant of the three vectors = A y + By + Cy arc tan A ( x + Bx + Cx ) The fourth vector required to achieve equilibrium is equal in magnitude and opposite in phase to the resultant of A, B, and C.
Translational Equilibrium / Vector Forces
page 2of 2
