Physics Honors Lab

Note: The two labs, Falling Bodies 1 and Falling Bodies 2, are similar in methods and the lab instructions may appear to be identical, but this isn't the case! The two labs have very different goals and important differences in procedure. Pay attention to the details in the instructions.

Uniform motion in one dimention, whether or not it is under constant velocity, is difficult to observe carefully. You must be able to mark the position of the falling object without actually affecting the motion of the object, so somewhat more sophisticated lab equipment is required than you usually find around the house.

We are going to use a somewhat imprecise method for comparing acceleration during free fall. In this lab, we will use multiple masses released simultaneously to determine whether mass affects the rate of descent. In doing this, we have to assume that the forces acting on the masses do not change during their descent, and that we can keep from introducing factors (differences in air friction, changes in mass, changes in horizontal velocity) which might cause the motion to vary from one drop to the next.

- Location where you have at least 10 feet (3 meters) for drop space.
*PARTNER*. You will need someone to help you observe the landing.- Masses to drop. You need at least two different, somewhat heavy masses with identical shapes and sizes, to avoid introducing factors such as air resistance. Avoid using very light objects such as ping pong balls.
- A drop tray filled with sand at least 2 inches deep.
- The usually paper and pencil to record your observations.
- Tape measure or other measuring device.

*Data Collection*

- Find the location and secure permission to perform you experiments from the appropriate authorities.
- Describe your masses. For example, if you use a ball, record its diameter, mass, anything you notice about it that may affect its fall rate.
- Record the distance from your release point to the ground (be sure to specify units!)
- Smooth the sand in the drop tray so that it presents a level surface.
- Drop your two different masses simultaneously. Make sure they land in your drop tray.
- Have your partner determine which mass struck the drop tray first (if either did).
- Measure the depth of the crater created in the drop tray by each mass.
- Repeat your observations at least five times.

*Data Reduction*

Arrange your data as you perform the reduction in some neat order, so that it is easy to see and understand what you have done. You may want to consider setting up a spreadsheet and letting it do the calculations for you. Here is a suggestion, but you can improve on it.

Mass | Drop1 | Drop2 | Drop3 | Drop4 | Drop5 | Mass landing first most often | Conclusion |

Which lands first? | 5kg | Unable to discern difference | 2kg | Unable to discern difference | Unable to discern difference | Neither | Masses accelerate at same rate |

Data Collection for crater depth

Mass | Drop1 | Drop2 | Drop3 | Drop4 | Drop5 | Average Depth | Standard Deviation |

Depth Mass #1 (5kg) in cm | 2.0 | 2.3 | 1.9 | 2.2 | 2.6 | 2.2 | 0.55cm |

Depth Mass #2 (2kg) in cm | 1.5 | 1.3 | 1.7 | 1.1 | 1.4 |

You will also need to determine the accuracy of your measurements. Physicists use a statistical method called determination of the standard deviation. According to this theory, 68.3% of all repeated measurments should fall within the standard deviation (plus or minus) from the average.

$$\sigma \text{}=\text{}\sqrt{\frac{1}{N-1}{\sum [{x}_{i\text{}}-\text{}\overline{x}]}^{2}}$$- σ is the standard deviation.
- N is the number of data points.
- x
_{i}is the i^{th}individual data point.

In the table above, the standard deviation for the 5kg mass is the square root of (1/5) * ((2.2 - 2.0)^{2} + (2.2 - 2.3)^{2} + (2.2 - 1.9)^{2}) + (2.2 - 2.2)^{2} + (2.2 - 2.6)^{2}) = 0.5477. So about 70% of my measurements should be within 0.55cm of the average 2.2, or between 1.7 and 2.7cm -- and they all are. The data above is valid.

- For each mass, determine an average crater depth based on your measurements.
- Determine the standard deviation for the measurement. If you have a scienctific calculator, you may follow the instructions for determining standard deviation on it.
- Do your observed values lie within one standard deviation of the average?

Your report should include:

- A description of your equipment and procedures which is sufficiently detailed that I could repeat your experiment myself to check your results.
- Your raw data and calculated data, with explanations of your asusmptions and calculations.
- Your conclusions about acceleration: is it constant?
- Your conclusions about force: is the force with which each mass strikes the ground the same? If not, how does it vary?
- A prediction: if you used an object two times the mass of your heaviest test object, would it strike the ground in less time falling from the same height? Would it create a crater with the same depth as your other masses?

Follow the instructions at the Moodle to post your lab reports where your fellow students can find them.

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