# Force Table

## 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 m1=0.100 kg on a string over a pulley attached to the force table at 0o. Place another mass m2=0.100 kg on a string over a pulley attached to the force table at 90o. 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/s2
• 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:
<!—->

 Student Name m1 [kg] F1 = (m1+mhook)(9.8 m/s2) [N] Angle (o) m2 [kg] F2 = (m2+mhook)(9.8 m/s2) [N] Angle (o) m3 [kg] F3 = (m3+mhook)(9.8 m/s2) [N] Angle (o)
• On a graph paper, draw vectors for that represent the two forces, F1 and F2.
• Use the vector addition rules to draw the vector that is the summ of the two: Fresultant = F1 + F2.

Activity 2:

• Repeat the experiment this time for two masses that are different. Place a mass m1=0.100 kg on a string over a pulley attached to the force table at 0o. Place another mass m2=0.150 kg on a string over a pulley attached to the force table at 90o. 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/s2
• 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:
<!—->

 Student Name m1 [kg] F1 = (m1+mhook)(9.8 m/s2) [N] Angle (o) m2 [kg] F2 = (m2+mhook)(9.8 m/s2) [N] Angle (o) m3 [kg] F3 = (m3+mhook)(9.8 m/s2) [N] Angle (o)
• On a graph paper, draw vectors for that represent the two forces, F1 and F2.
• Use the vector addition rules to draw the vector that is the summ of the two: Fresultant = F1 + F2.

Questions

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

• Compare the force F3 that balances the forces F1 and F2 (your experimental result) with the resultant vector Fresultant from the vector addition (your theoretical result).

Compare their magnitudes.

Compare their direction.