# Force Table

## Force Table: Balance of Forces

#### Purpose

To determine the force that balances two other forces applied on an object.

Objectives

• To learn how to use vectors to represent physical forces.
• To become proficient in drawing vectors and adding them graphically
• To learn proficient in calculating force components from magnitude and direction
• To learn learn how to apply conditions for equilibrium of forces.

#### Equipment

• Force table with a ring, set of weights,
• Three hooks with pulley clamps and strings
• Mass scale
• Graphing paper

#### Theory

If a 2-dimensional vector $\vec{A}$ has magnitude of $A$ and direction given by an angle θ measured from the positive x axis, then its components are given as: $A_x = A\cos \theta\;\;\;\;\;A_y = A\sin \theta$

Alternatively, if you know the components of the vector, $A_x$ and $A_y$, then the magnitude and angle are given as: $A=\sqrt{A_x^2+A_y^2}\;\;\;\;\;\theta=\arctan \frac{A_y}{A_x}$

Remember!  Check the quadrant the location of angle θ. The calculator will give you answers either in I-st or IV-th quadrant. If that is not the case, you will have to add 180o.

#### Setup Attach strings to the ring and place the ring at the center of the Force Table.

Place 150 g on a 50-g hook (for a total of 200 g) and hang it at 30o

Place 100 g on a 50-g hook (for a total of 150 g) and hang it at 135o

#### Experiment

Determine the tension in the third string and at what angle so that the ring is balanced, that is it is at the exact center of the table.

A. Angle

Hold by hand and pulling the third string at different angles until you determine at what angle the ring is balanced.  Write it down.

B. Tension

Set up the last pulley clamp at the angle, and hang the 50-g hook on the string. Add weights until the ring is balanced. Record the total mass hanging.

#### Calculations

Record the magnitude and direction of all three forces. Calculate their x- and y- components.

Force Hanging Mass Magnitude Direction Fx Fy
1 200 g
2 150 g
3

#### Analysis and Assignments

A1. Add all three x-components, and all three y-components.

Question: Is the total x-component equal to zero? Is the total y-component equal to zero?

A2. Draw $\vec{F}_1$ and $\vec{F}_2$ on graphing paper. Using the parallelogram rule, draw their sum $\vec{F}_{\text{sum}}$

Question: Is the vector for the third force $\vec{F}_3$ equal in magnitude but opposite in direction to the sum $\vec{S}$