Lab #4: Force Table Lab
Purpose:
The purpose of the lab is to gain experience with working with vectors and vector quantities through the addition of several vectors to find a resultant vector.
Equipment:
- Force Table
- Masses
- Pulleys
- String
- Metric Ruler
- Protractor
- Graph Paper
Procedure:
Experimental:
Place a pulley at the 30 degree mark on the Force Table and place a total of 0. 35 kg (which includes 0.05 kg of the mass holder) on the end of the string. Place second pulley at the 130 degree mark and place a total of 0. 25 kg (including 0. 05 kg of the mass holder). Calculate the magnitude of the forces produced these masses and record them in Table 1. Determine by trial and error (See Appendix) the magnitude of mass needed and the angle at which it must be placed in order to place the ring in equilibrium. The ring is in equilibrium when it is centered on the Force Table. Be sure that all the strings are in such a position that they are directed along a line that passes through the center of the ring. From the experimentally determined mass, calculate the force produced and record the magnitude and direction of this equlibrant force in Table 1. From the value of the equlibrant force, determine the magnitude and direction of the resultant force and record them in Table 1.
Graphical:
Find the resultant of these two applied forces by scaled graphical construction using the parallelogram method (See Appendix). Using a ruler and a protractor, construct vectors whose scaled length and direction represent F1 and F2. A convenient scale might be 1 graphical division = 0. 1 N. Read the magnitude and direction of the resultant from your graphical solution and record them in Table 2.
Analytical:
Using equation 1, calculate the components of F1 and F2 and record them into the analytical solution portion of Table 3. Add the components algebraically and determine the magnitude of the resultant by the Pythagorean Theorem. Determine the angle of the resultant. (See Appendix) Calculate the percentage error of the magnitude of the experimental value of FR compared to the analytical solution of FR. Also calculate the percentage error of the magnitude of the graphical solution of FR compared to the analytical solution.
Collected Data:
Experimental:
Force | Mass (kg) | Force (N) | Direction |
---|---|---|---|
F1 | .35 kg | 3.4335 N | 30 |
F2 | .25 kg | 2.4525 N | 130 |
Equilibrant FE | .395 kg | 3.87495 N | 250 |
Resultant FR FR | .395 kg | 3.87495 N | 70 |
Graphical:
Force | Mass (kg) | Force (N) | Direction |
---|---|---|---|
F1 | .35 kg | 3.4335 N | 30 |
F2 | .25 kg | 2.4525 N | 130 |
Resultant FR FR | .373768 kg | 3.667 N | 68 |
Analytical:
Force | Mass (kg) | Force (N) | Direction | X-Component | Y-Component |
---|---|---|---|---|---|
F1 | .35 kg | 3.4335 N | 30 | 2.9735 N | 1.17675 N |
F2 | .25 kg | 2.4525 N | 130 | -1.57664 N | 1.87872 N |
Resultant FR | .393206 kg kg | 3.85735 N | 68.7658 | 1.39706 N | 3.49547 N |
Data Analysis:
Error Calculation:
Percent error magnitude experimental compared to analytical =
[(Experimental – Analytical)/Analytical] x 100% = .4563%
Percent error magnitude graphical compared to analytical =
[(Graphical – Analytical)/Analytical] x 100% = 4.94251%
[(Experimental – Analytical)/Analytical] x 100% = .4563%
Percent error magnitude graphical compared to analytical =
[(Graphical – Analytical)/Analytical] x 100% = 4.94251%
Conclusion:
- Possible sources of errors include 1) friction in the pulleys, 2) the fact that
we ignored the mass of the strings, and 3) errors in direction of the
forces if the strings were not at 90 degrees to the tangent to the ring.
Rank the relative importance of these errors in your data. - #3,
#2, #1 - If pulleys were not used, would
the errors have gone up? Why? - Yes, as with the
removal of the pulleys would have increased the friction present in the system,
which in turn would have increased the amount of force ignored in the
calculations, thus increasing the error.
References:
Experimental (trial and error) Method:
Add the required third force F3 calculated from the above methods to balance the other two forces. The ring should remain centered. If not, then change the direction and/or amount of the third force until it does. This balancing force is called the equilibrium force and it is equal in magnitude and opposite in direction to the resultant force of F1 and F2. Note the difference between the values and directions of F3 that you obtained experimentally and theoretically (using graphical and component methods).
Parallelogram Method:
Using a protractor and a ruler, draw arrows to represent the forces F1 and F2. Remember that you must choose a scale so that the length of each arrow is proportional to the magnitude of the force, and the direction of each arrow must be the same direction as the force it represents. Use either head-to-tail method or parallelogram method to draw an arrow that represents the resultant of the vectors. Measure the length of
the arrow, determine the magnitude (size) of the resultant and its direction. To balance F1 and F2, you will need to apply a force F3 whose magnitude is equal to this resultant force, but opposite in direction.
Component
Method:
With your calculator, determine the x and y components of F1 and F2. Remember that Fx = Fcos q
and Fy = F sin q. Find the x and y components of the resultant from the sum of x and y components. Draw a right triangle with x and y components as sides, and the hypotenuse representing the resultant. Calculate the magnitude of the resultant from the square root of (Rx2 + Ry2). Calculate
the direction of the resultant by using q R = tan-1 (Ry/Rx). Does this result agree with the graphical method?
Add the required third force F3 calculated from the above methods to balance the other two forces. The ring should remain centered. If not, then change the direction and/or amount of the third force until it does. This balancing force is called the equilibrium force and it is equal in magnitude and opposite in direction to the resultant force of F1 and F2. Note the difference between the values and directions of F3 that you obtained experimentally and theoretically (using graphical and component methods).
Parallelogram Method:
Using a protractor and a ruler, draw arrows to represent the forces F1 and F2. Remember that you must choose a scale so that the length of each arrow is proportional to the magnitude of the force, and the direction of each arrow must be the same direction as the force it represents. Use either head-to-tail method or parallelogram method to draw an arrow that represents the resultant of the vectors. Measure the length of
the arrow, determine the magnitude (size) of the resultant and its direction. To balance F1 and F2, you will need to apply a force F3 whose magnitude is equal to this resultant force, but opposite in direction.
Component
Method:
With your calculator, determine the x and y components of F1 and F2. Remember that Fx = Fcos q
and Fy = F sin q. Find the x and y components of the resultant from the sum of x and y components. Draw a right triangle with x and y components as sides, and the hypotenuse representing the resultant. Calculate the magnitude of the resultant from the square root of (Rx2 + Ry2). Calculate
the direction of the resultant by using q R = tan-1 (Ry/Rx). Does this result agree with the graphical method?