Name
PHY107

## How does the distance from the edge change as the mass hanging over the edge changes when trying to get the box to stop exactly at the edge?

#### Exploration Phase

The Launch: A box with some weights in it is placed on a table. A string is connected to the front of the box and placed over the edge of the table. A weight is connected to the end of the string that is hanging over the table. When the box is let go it starts to slide toward the edge of the table. When the box gets to the edge of the table it stops. After that demonstration each group was asked to use the available materials and replicate the demonstration.

As part of trying to model the box stopping at the edge, a variety of materials and weights were used. Three blocks of wood and a metal block were used to model the box. The maximum distance that the block could be pulled back from the edge, without the block going off of the table at the edge, was determined for each block and weight combination. The following data was collected:

"Box"Distance From EdgeTotal Mass on
Top of the Table
Mass Hanging From
the End of the String
Metal Block10.5 cm253.5 g113.5 g
Wooden Block20.5 cm118.1 g70.1 g
Wooden Block8 cm101.7 g114.5 g
Wooden Block
(Wax on Bottom)
18.5 cm148 g114 g

The exploration and this data suggest the following questions.

1. Why does the box stop at the edge?
2. What influence does the material sliding along the table have?
3. How does the maximum distance from the edge change as the mass on top of the table changes?
4. How does the maximum distance from the edge change as the mass hanging over the edge changes?
5. How does the distance from the edge change as the mass hanging over the edge changes when trying to get the box to stop exactly at the edge?
6. What forces are acting on the box?

For this investigation the question "How does the distance from the edge change as the mass hanging over the edge changes when trying to get the box to stop exactly at the edge?" was chosen.

#### Experimentation and Data Collection

The objective of the experiment was to determine if there is a connection between the amount of mass on the end of the string and the distance from the edge of the table that is necessary to get the box to stop exactly at the edge. Collecting data for the mass on the end of the string and the corresponding distance from the edge that allows the block to stop at the edge will show any pattern if one exists.

For this experiment the same block will be used for each trial, but the amount of mass on the end of the string will vary. For each mass the distance from the edge that causes the block to stop at the edge will be determined. Two sets of data were obtained, one for a wooden block and the other for the wooden box.

Data for Wooden Block
Mass (grams)Distance (cm)
2054
2525
3019
3514
4013
4511.5
5010
559.5
608.5
658.2
708
757.5
807.2
857
907
956.8
100Tips Over
Data for Wooden Box
Mass (grams)Distance (cm)
5546
6018
6512
709
758
807
856.5
906
955.5
1005
1055
1104.5
1204.5
1254
1454
1503.7
1553.5
1953.5
2003
600Tipping Over

#### Making Sense

The data shows a general trend where the larger the mass on the end of the string, the shorter the distance from the edge to get it to stop at the edge.

Result: The larger the mass, the shorter the distance.

The general trend is clear, even with this rough data. Better, more carefully obtained data would not likely change the overall conclusion. A prediction is that a very large mass would result in a very short distance. An unexpected aspect of the data was that the distance dropped quickly and then leveled off. Notice that large changes in the hanging mass doesn't change the distance toward the end of the box experiment. More careful measurements after it starts to level off would be in order and would give more confidence in the result.

The following analysis uses well-known physics principles (see a physics book). The horizontal force that the string is exerting on the box to slide it toward the edge is due to the hanging mass at the end of the string. Friction is opposing the horizontal force of the string. A large hanging mass provides a large horizontal force. When an object at rest has an unbalanced force acting on it, the object will begin to move. The longer the unbalanced force is acting on the object, the faster the object will move. Fast moving objects are harder to stop than slower moving objects. A large hanging mass will provide a big unbalanced horizontal force that could make the box move very fast in a short distance. With such a large unbalanced force, to get the box to stop at the edge it can only be placed a short distance from the edge. With less hanging mass the unbalanced force is smaller and the box can be placed farther back from the edge.

At the edge of the table the string is hanging directly downward and there is no longer any force pulling the box horizontally (horizontal and vertical forces are independent of each other) and so the box will not be pulled horizontally after reaching the edge of the table (there is no longer any unbalanced horizontal force). This explains why the box can stop at the edge.

The experiment could be improved by controlling the conditions better, making sure that the top of the table and the bottom of the slider were clean, for instance. The distance measuring device should be improved and the hanging masses could be cleaned and recalibrated. Improving these conditions, however, would not likely change the overall result of the investigation. New questions from this investigation could be:

1. What is the shape of the curve?
2. Why do you need less distance with more mass?
3. Why does the box move faster when the mass on the string is higher and the distance is shorter?
4. What is the relationship between the speed of the box and the amount of hanging mass?
5. Is it significant that the distance levels off as the hanging masses get higher?
6. Does the distance go to a constant value or does it get close to zero as the mass gets very large?