 Lab Force Table - Force Vectors in Equilibrium
Purpose: In this lab you are going to investigate static equilibrium produced by three concurrent forces.

To complete the lab you will need the following equipment: a force table, one washer with its three attached strings, three pulleys, and a set of hooked masses (10-500 grams).

Procedure

The first task is to attach all three strings through the washer. We will do this by folding the string in half, passing the folded end into the washer, and threading the rest of the string through the fold. Tie a knot at the end of the strings. These knots will support the hooked masses. Finally arrange the three string-loops around the washer, but do not tighten them - let them be free to move along the circumference of the washer.  At the end of each string you will attach a hooked mass: 10 grams, 50 grams, 100 grams, 200 grams or 500 grams. Each string must have a different amount of mass – no duplicates. Adjust the positions of the strings so that the central ring is in static equilibrium. The inner circumference of the ring should be equally spaced around the center “hole.” No strings may lie along angles that are multiples of 30º or 45º. Initially start you’re your largest mass attached to a string which passes over a pulley at 0º. Then add a second mass to a second pulley placed at any arbitrary position (remember to not use any of the restricted angles). Then start “playing” with the amount of mass needed and the angles needed to keep the center of the washer over the “hole.” No masses may be added to your greatest mass at 0º - otherwise you can move masses around as needed. When the system appears to be in equilibrium, please the third string over its pulley for a final test. Adjust as necessary.

Check Point (1): Gently displace the washer and make sure it returns to equilibrium before recording your data.

Check Point (2): Are the forces (the weights of the attached masses) all unique?  (Yes/No)  Remember that you are not allowed to have any duplicate values.

When equilibrium is confirmed, record the positions (in degrees) of each string and the amount of mass suspended from each string in the following table.

 table angle attached mass equivalent force string (degrees) (g) (N)
 1
 2
 3

Complete a scaled vector force diagram using the head-to-tail method of vector addition. Make sure to not rotate your diagram as all “relocated origins” must have their x-axes parallel to the original x-axis for your 0º force.  Use a scale of 5 cm = 1 N. Placing each force vector at its appropriate angle and drawn to its proportional length. LONGER vectors produce better results. Check Point (3): Based on your scale of 1 N being represented by 5 cm, are each of your vectors drawn to the correct length and at the correct angle? Label your vectors with their lengths and directions (using counterclockwise angles measured from the positive-x-axis) as ordered pairs. Make sure that each force vector terminates with an arrow.

If your vectors do not “close on each other” construct and measure the “required” 4th vector to establish equilibrium. Label it on your diagram as an ordered pair. Highlight this vector in a second color.

Make sure that you diagram is correctly scaled and labelled before continuing on to the next section. Remember that each person in the group is to complete their own diagram. Consequently, the 4th vector may have slightly different values depending on the skill of the “draftsman.”

Using a calculator that has trig functions (making sure that it is set in degree mode), complete the following table. In the first column report the length (len) and direction (dir) from your vector diagram. Next calculate the x- and y-components of each vector to 2 decimal places. Include both the positives and negatives values

 x = Lcos(θ) y = Lsin(θ) vector (len, dir) (cm) (cm)
 1
 2
 3
 4

NOTE: If your diagram was constructed and measured correctly, the values for both net-x and net-y should both zero.

Refer to the following information for the next two questions.

Conclusions

 Why did the value of the 3rd hanging mass change once its string was placed over its pulley in your final test?

 Why do you think your group’s data was “destined” to need the 4th vector to truly set your washer into a state of equilibrium?

Refer to the following information for the next two questions.

The strong man can withstand the tension force exerted by the two horses pulling in opposite directions. How would the tension compare if only one horse pulled and the left rope were tied to a tree?

 How would the tension compare if the two horses pulled in the same direction, with the left rope tied to the tree?

Refer to the following information for the next two questions.

The right puppy is pulling on the shoe with a force of 40N at an angle 24º and the left puppy is pulling on the shoe with a force of 55N at 141º. SHOW ALL CALCULATIONS. You may either use the calculator method or a scaled diagram. If you use a diagram, make sure to inform the reader of your scale.

 If the shoe’s owner adds a third force to place the shoe into a state of static equilibrium before trying to extract the shoe from the two dogs, then what size force and should she attempt to rescue her shoe?

 At what angle should she apply the force in your previous answer?

Make sure to turn in a copy of the final conclusion's calculations AS WELL AS your original force-table diagram to your instructor.