The Force Table

Theory

Physics: Force and net-force. Math: vector addition.

Vocabulary

Force table - a lab table with a protractor marked along the edge. The protractor eases measuring angles. It is used to demonstrate the vector nature of forces, namely: the weights of masses suspended from the table by threads (Figure 1).

Resultant - vector that is a sum of two (or more) other vectors.

Equilibrant - vector that balances the two given forces. An equlibrant is equal to the resultant, but has an opposite direction. See the diagram below:

Experimental procedure

The table

In order to perform this experiment, first you need to to prepare the table.

1. Level the table. Use the three adjustment screws under its legs.

2. Fasten three strings to the ring and secure the ring over the center of the table using a pen or pencil.

3. Attach weights to the strings. Use pulleys to minimize friction. Place pulleys at 0, 120, and 240 degree.

4. Test for equilibrium: carefully remove the pen/pencil while watching the ring. If the ring is still in its central position, then the system is in equilibrium.

Error of the Force Table experiment

1. To find the error, add the smallest weight on one side. If the system is still in equilibrium, add another one.

2. The maximum weight that can be added while the system is still in equilibrium indicates the accuracy of the experiment – the experimental error.

Part 1

Place pulleys 1 and 2 according to the Table 1 in the Lab Report. Add the same mass to both pulleys. Find the equilibrant by adding weights to the third pulley.

In the next step, find the resultant using either calculations (the cosine law should be helpful; can be the one offered by Google here) or a graphical method (add the vectors on paper and measure the resultant). You can also go to this website to add two vectors. Write down the results in Table 1a. Let 1 cm in the vector magnitude represent 1 gram of mass in your graphical method (eg. a weight of 50 g is represented by 50 cm).

Part 2

In the second part of the lab, the masses of the two original vectors are not equal (see Table 2 in the Lab Report). Therefore, it will be useful to do the calculations first in order to find both the mass and the direction of the resultant. Use the calculated sum to adjust pulleys at the force table. The equilibrant is opposite to the resultant so either add or subtract 180 degree to find it.

Find the resultant using any method of vector addition. Write down the results in Table 2.

Place all three pulleys according to your findings; hook the proper masses on pulley 1 and 2. Find the equilibrant by adding weights to the third pulley.

Error

Both parts require the percent difference between the resultant and equilibrant. You can follow the formula:

...or go to this website to calculate it. Even the difference usually accepted in this lab is 3%, some of our students presented measurement of 0.01% difference using only graphical method of vectors addition. Kudos!

DO NOT HESITATE TO ASK if you have any questions.