## Force Table

**Purpose: To investigate what is the effect of multiple forces on a single object. **

**Objectives**

- To balance forces so that an object is in equilibrium.
- To learn how to use vectors to represent forces.
- To learn how to add forces using the vector addition rules.
- To learn how to draw vectors to scale on a graph paper.
- To distinguish between experimental observations and theoretical predictions.

**Equipment**

- Force Table
- Pulleys
- Center Ring with strings attached
- Set of calibrated masses
- Graphing Paper

**Theory**

When we talk about forces, it is important that we know their magnitude (strength) and their direction. It is impossible to use numbers for forces, as numbers do not show any directions. We must use different mathematical quantities, called **VECTORS** to represent forces

Vectors are drawn as arrows, where their length is called “magnitude”, and the direction of the arrow is the direction of the vector. The arrow side is called the “tip” of the vector, and the other side is called its “tail”. Here is an example of a vector called A:

A person with mass 50 kg will have a weight equal to (50)x(9.8)=490 N. The force of the weight points “down” towards the center of the Earth. Here is a vector **W** that can represent that weight:

The question now is: “How shall we represent the resultant force”. In other words, if there are two or more forces acting on an object, what will be the total effect in terms of force? It turns out that if we were to use the mathematics vector addition rules and draw a vector that is the sum of all the vectors, that vector will have both magnitude (strength) and direction identical to those of the resultant force.

Grahical Addition of Vectors. There are generally two rules (which are really one rule, only they appear different) to add vectors. The **Tip-To-Tail Rule** is applied when the tip of vector F coincides with the tail of vector W. When both vectors tails coincide, we apply the **Parallelogram Rule**. Both rules are illustrated on the picture below:

Note that in both diagrams, the resultant vector **F+W** comes out with the same length (magnitude) and direction, hence both rules are identical. It is a matter of convenience which rule we use to draw the resultant vector.

**Experiment, Data and Results**

**Activity 1:**

We will balance a ring that is being pulled by several strings attached to different weights.

- Place a mass m
_{1}=0.100 kg on a string over a pulley attached to the force table at 0^{o}. Place another mass m_{2}=0.100 kg on a string over a pulley attached to the force table at 90^{o}. Calculate the force of gravity on each of the hanging masses (don’t forget to include the mass of the hooks) by multiplying the mass times the gravitational acceleration g = 9.8 m/s^{2} - Here is a picture of how the force table should be set up:

- Determine where and how much you have to pull to cancel the pulling of the two forces. Write down all the masses, forces, and the corresponding angles in a table:

- On a graph paper, draw vectors for that represent the two forces, F
_{1}and F_{2}. - Use the vector addition rules to draw the vector that is the summ of the two: F
_{resultant}= F_{1}+ F_{2}.

**Activity 2:**

- Repeat the experiment this time for two masses that are different. Place a mass m
_{1}=0.100 kg on a string over a pulley attached to the force table at 0^{o}. Place another mass m_{2}=0.150 kg on a string over a pulley attached to the force table at 90^{o}. Calculate the force of gravity on each of the hanging masses (don’t forget to include the mass of the hooks) by multiplying the mass times the gravitational acceleration g = 9.8 m/s^{2} - Determine where and how much you have to pull to cancel the pulling of the two forces. Write down all the masses, forces, and the corresponding angles in a table:

- On a graph paper, draw vectors for that represent the two forces, F
_{1}and F_{2}. - Use the vector addition rules to draw the vector that is the summ of the two: F
_{resultant}= F_{1}+ F_{2}.

**Questions**

- How did you know that the ring is in equilibrium?