The Force Table

w/Force Sensor

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:

Resultant and Equilibrant marked on vector addition diagram

Experimental procedure

Setting the table

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

Level the table (the marble ball test). Use the three adjustment screws under its legs.
Fasten the strings to the ring and secure the ring over the center of the table using a pen or pencil.
Attach weights to the strings. Use pulleys to minimize friction.
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.

Force table with two masses suspended and secured by a pencil holding the ring in a central position

Figure 1. Force table and two masses suspended.

Figure 2. Pulley.

Ring secured with a pencil on a force table

Figure 3. Ring secured with a pencil.

Figure 4. Mass suspended from the table by a thread.

The measurement technique

In order to measure force with the force sensor, place the sensor on the table and hook it to the ring (Figure 5). To read the force value, you must hold the sensor so it does not touch the security pencil (Figure 6). Otherwise, the sensor will read two weights minus the tension in the pencil (as shown in Figure 5).

Figure 5. The force sensor hooked to the ring. Notice that the ring touches the security pencil; hence, the reading of 0.230 N is incorrect.

Figure 6. The force sensor hold for measurement. Notice that the ring does not touch the security pencil; hence, the reading of 1.859 N is correct.

A. Fixed Angles

Place pulleys 1 and 2 at 40^o and 320^o. Hook masses indicated in Table 2 (see the Worksheet) to both pulleys.
Calculate the magnitude and angle of the resultant (or go to this website to calculate it). Remember to multiply the calculated magnitude by g = 9.81 m/s² (Why?). Write down the calculated value in the Resultant Force column.
Make sure the Force Sensor is placed along the direction indicated by the resultant. Read the equilibrant’s magnitude on the sensor. Write down the reading in the Equilibrant Force column.

B. Fixed Mass

Place pulleys 1 and 2 at positions indicated in Table 1 in the Worksheet. Hook the same masses, e.g. 150g, to both pulleys.
Calculate the magnitude and angle of the resultant (or go to this website to calculate it). Remember to multiply the calculated magnitude by g = 9.81 m/s². Write down the calculated value in the Resultant Vector column.
Place the sensor at 180^o. Read the equilibrant’s magnitude on the sensor. Write down the reading in the Equilibrant Force column.

Percent Difference

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

C. F = f(Ɵ) Investigation

Place pulley 1 at 0^o and pulley 2 at 350^o. Hook identical masses to both pulleys.
Read the equilibrant’s magnitude on the sensor. Note: Always place the Force Sensor along the direction indicated by the resultant (Figure 7).
Write down both the angle and the magnitude of the equilibrant in Table 3 in the Worksheet.
Take several measurements at various angles (See Table 3).
Plot the results.
Draw conclusions based on the graph.

Placing the Force Sensor on the axis of symmetry

Figure 7. Placing the Force Sensor.

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