# Center of Mass

## Center of Mass

The center of mass of a body or object is also referred to as the center of gravity of the object. The center of mass of a body is the point of mass distribution within or outside the body where the weighted relative position of the object sums to zero. An experiment to identify the center of mass for an object aims at identifying the point of balance of an object. The objective of experiment is to identify the point at which a body looses balance and falls.

In this project we will be testing the center of mass project of a stack of books that are stacked together from the edge of a table. The items we will be using include:

1. 6 Identical text books A5 size(21cm by 14.8cm)
2. 6 empty CD cases
3. A measuring ruler
4. Table
5. Pen/Pencil

### Procedure

1. Place the first book on the edge of the table and measure the distance, d, that overhangs the edge of the table and record the reading in the results table.

2. Add another book on top of the first book with a slightly longer distance, d. i.e

3. Repeat the above experiment by stacking up a single book with a slightly longer distance, d. and add the readings to the results table.
4. Mark the last point where the 6th book topples over.

## Results Tables

### The experiment using the 6 books:

#### The first trial

 No Book Distance, d (cm) Comment 1 Book1 0 No toppling 2 Book2 0 No toppling 3 Book3 0 No toppling 4 Book4 0 No toppling 5 Book5 0 No toppling 6 Book6 0 No toppling

Note: This is the control experiment with in this set up. It is used as the referencing point where the center of mass of the whole stack of books is at the center of the stack and is directly on the table.

#### The second trial

 No Book Distance, d (cm) Comment 1 Book1 1 No toppling 2 Book2 2 No toppling 3 Book3 3 No toppling 4 Book4 4 No toppling 5 Book5 5 No toppling 6 Book6 6 No toppling

#### The third trial

 No Book Distance, d (cm) Comment 1 Book1 2 No toppling 2 Book2 3 No toppling 3 Book3 4 No toppling 4 Book4 5 No toppling 5 Book5 6 No toppling 6 Book6 7 No toppling

#### The fourth trial

 No Book Distance , d (cm) Comment 1 Book1 3 No toppling 2 Book2 4 No toppling 3 Book3 5 No toppling 4 Book4 6 Stack Topples 5 Book5 - - 6 Book6 - -

## Summary of the experiment with books

In the first trial, the distance from the edge cannot change to ensure that the center of the mass remains at the center and the weight evenly distributed with respect to the position on the table.   In the experiment, the center of the mass of the book is tested by changing the overlap distance from the edge of the able of the mass. This is done by varying the surface area covered by stack while shifting and adding weight to one side of the stack.  The stack then falls when the center of the mass shifts to outside the base surface area which is the area covered by the first book on the surface of the table.

The distance that produces the longest distance, d, from the edge of the table without toppling over is in the first try where the first book is placed the shortest distance from the edge of the table, 1cm (Assis, 2010). This allowed the 6th book to extend up to 6cm, the greatest overhang, from the edge of the table. The stability of the stack majorly depends on the length of the first book of the edge of the table. When the distance reduces the distance, d, at which the stack falls increases hence stability. Trying 100 books would be almost impossible and if it has to work there would no significant variation in the distance, d, from one book to the next in the stack.

### The first trial

 No CD case Distance, d (cm) Comment 1 Case1 0 No toppling 2 Case 2 0 No toppling 3 Case 3 0 No toppling 4 Case 4 0 No toppling 5 Case 5 0 No toppling 6 Case 6 0 No toppling

Note: This is the control experiment with in this set up. It is used as the referencing point where the center of mass of the whole stack of CD Case is at the center of the stack and is directly on the table.

#### The second trial

 No CD case Distance, d (cm) Comment 1 Case1 0.5 No toppling 2 Case 2 1.0 No toppling 3 Case 3 1.5 No toppling 4 Case 4 2.0 No toppling 5 Case 5 2.5 No toppling 6 Case 6 3.0 No toppling

#### The third trial

 No CD case Distance, d (cm) Comment 1 Case1 1.0 No toppling 2 Case 2 1.5 No toppling 3 Case 3 2.o No toppling 4 Case 4 2.5 No toppling 5 Case 5 3.o No toppling 6 Case 6 3.5 No toppling

#### The fourth trial

 No CD case Distance , d (cm) Comment 1 Case1 1.5 No toppling 2 Case 2 2.o No toppling 3 Case 3 2.5 Stack Topples 4 Case 4 - - 5 Case 5 - - 6 Case 6 - -

## Summary of experiment with the use of empty CD cases.

The distance that produces the longest distance, d, from the edge of the table without toppling over is in the first try where the first CD case is placed the shortest distance from the edge of the table, 1cm. This allowed the 6th CD case to extend up to 6cm, the greatest overhang, from the edge of the table. The stability of the stack majorly depends on the length of the CD case of the edge of the table. When the distance reduces the distance, d, at which the stack falls increases hence stability (Cutnell & Johnson 1998). Comparing the CD case experiment to that done with books we can generally conclude that the weight of the object also has a major influence on the ratio of the overhang distance.