Lab #2 - The Force Table
Copyright R. Mahoney 2013
Name: _______________
The purpose of this lab is to demonstrate how vectors add, and to use the
Principle of Orthogonality. The letters gm stand for grams.
1. Set up your force table as shown in class. Use a level to make sure that your
table is horizontal.
Q1: Does your force table really have to be horizontal?
2. You will be balancing three forces (which are vectors), so you need to "weigh"
the weight holders for the weights you will put on them. Use a balance beam
scale to determine their weights (in mass equivalent grams). Mark your weight
holders by putting masking tape on their bottoms and writing the numbers 1, 2
and 3.
Weight, holder 1: ______ Weight, holder 2: ______ Weight, holder 3: ______
Q2: Why can we write something's weight down in grams, as opposed to
Newtons?
3. Set up the three pulley wheels at the following angles: 0º, 90º, and 233º. Add
the nominal weights of 100 gm to weight holder 1, and the nominal weight of 150
gm to weight holder 2. Place the combined weights on the strings going over the
0º and 90º pulleys, for weight holders 1 and 2 respectively.
Combined weight in gm going over pulley at 0º : __________ (weight holder 1)
Combined weight in gm going over pulley at 90º : __________ (weight holder 2)
4. Put weight holder 3 on the string going over the 233º pulley, and start adding
weights until a rough balance (null condition) is achieved. (A balance is achieved
when the ring is centered over the pin in the middle of the force table, and it
returns to its centered position, quivering, when perturbed.) Once a rough
balance is achieved, move the 233º pulley a small number of degrees each way,
until you are sure you have found the correct angle for the restoring force to be
equal and opposite to the resultant of the two weights over the 0º and 90º
pulleys. Try adding or subtracting a gram or two to force 3, as needed, , to be
sure you have found the best experimental values for the magnitude and angle of
the restoring force, or equilibrant, the force that cancels out the resultant of
forces 1 and 2.
Combined weight in gm going over pulley at nominal 233º : __________
This is your experimental value for force 3.
Actual angle of pulley at nominal 233º : __________
5. Use the quadrille notepaper supplied, graph the theoretical addition of forces
1 and 2 (weights over pulleys at 0º and 90º respectively). This is your resultant
vector.
(The theoretical addition of the vectors will be done in the next step, using
trigonometry: this graph is only "for show".)
Looking at your graph, what should the magnitude and direction of your restoring
force, force 3, be? Show and label this vector on your graph too. Attach your
graph to your final report.
6. Setting the 0º direction as the plus x axis, and the 90º direction as the plus y
direction, insert forces 1 and 2 (expressed in gm) into the chart below. Using the
Principle of Orthogonality, determine what the theoretical x and y components of
force 3 must be.
Force
x component (gm)
y component (gm)
_______________
_______________
0 gm
0 gm
Force 1, pulley 0º
Force 2, pulley 90º
Force 3, pulley 233º
(theoretical)
Totals
7. Use the theoretical x and y values of force 3 just determined to calculate the
theoretical magnitude of force 3. What is it?
Force 3, theoretical: __________ gm
8. Determine the percent error between the theoretical and experimental magnitudes
of force 3.
Percent error, magnitude of restoring vector: __________ %
9. Imagine setting up the three pulleys at 0º, 120º and 240º, with added weights
of 100 gm at 0º and 240º. What weight must be added at 120º to obtain the null
condition? What is this scenario an example of?
Weight at 120º: __________ gm
Scenario is an example of: