Lab Assignment 1: Linear Motion

Instructor’s Overview

This lab experiment focuses on freely falling objects. We developed the kinematic equations for freely falling objects in Module 2. Now we will have an opportunity to directly experiment with free fall and apply our quantitative knowledge of kinematics.

This activity is based on Lab 6 of the eScience Lab kit. Although you should read all of the content in Lab 6, we will be performing a targeted subset of the eScience experiments.

Our lab consists of two components. These components are described in detail in the eScience manual (pages 71-73).

This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations.

EXPERIMENT 1: Time vs Distance of a Dropped Object.

Reference: Section 2-7 in your text.

Theory: When a object is dropped the magnitude of its velocity (speed) increases as it is accelerated by the force of gravity. Assuming air friction is negligible all objects will have accelerated (increase their speed) by 9.8 m/s every second. At the end of 1 second the speed is 9.8 m/s, at the end of 2 seconds the speed is 19.6 m/s, etc. This acceleration, the acceleration due to gravity is named g. We write this as 9.8 m/s per second, which then becomes 9.8 m/s/s and then 9.8 m/s². We say g is 9.8 meters per second squared.

For a falling object the following equations prevail:

y = ½ g t² and t =

y is the distance dropped and t is the time from releasing the object until it hits the floor. Note other letters are sometimes used for the variable, d being a popular choice.

Procedure:

You will drop one of the hex nuts from a height of about 6 ft. Stand near a wall, door jam, post of some kind and place a tape or have some other way of marking the height you will drop the hex nut from. Record this height.

With a stop watch time the drop of the hex nut and record in the data table below. Repeat this for a total of 10 trials.

Height of Drop: ___________

Data table for hex nut drop experiment:

Drop Number	Time (sec)
1
2
3
4
5
6
7
8
9
10
Average
Standard Deviation

Calculations:

Using the average time from the table calculate the distance the hex nut dropped and compare to your recorded distance. Discuss sources of error. What does the Standard Deviation of your table imply? By-the-way, average reaction time for most people is about 0.2 seconds. That implies if you are driving and see a change in the traffic light it will take 0.2 seconds before your foot begins to move.

EXPERIMENT 2 – Time intervals of a series of dropped objects.

In this experiment you will make two strings of separated hex nuts and explore the interval of time between the impacts on the floor.

:

Construction:

String 1: Evenly spaced hex nuts:

d = 0.1 m (10 cm). Tie the first nut 10 cm from the end of the string and then continue tying hex nuts 10 cm above the previous until 6 hex nuts are tied to the string.

Record the distance the hex nut is from the end of the string; this will be the distance the hex nut falls to the floor.

Hex Nut	Y (m)
1	0.1
2
3
4
5
6

Procedure:

Consider placing a pan lid, plate, or perhaps aluminum foil on the floor to make the impact sound louder.

With the end of the string just touching the floor and you holding up the extended string drop the string and listen to the impacts.

Results: Record your observation of the impacts. Do the succeeding impacts occur in equal time intervals or are the time intervals different and if so how?

String 2: Unevenly space hex nuts:

d = 0.1 m (10 cm). Tie the first nut 10 cm from the end of the string and then continue tying hex nuts with the spacing of: 30 cm, 50 cm, and 70 cm.

Again record the distance the nuts are from the end of the string. This will be the distance they fall to the floor.

Hex Nut	Y (m)
1	0.1
2
3
4

Procedure:

With the end of the string just touching the floor and you holding up the extended string drop the string and listen to the impacts.

Results: Record your observation of the impacts. Do the succeeding impacts occur in equal time intervals or are the time intervals different and if so how?

What was the difference between the noise patterns for equally spaced nuts compared to the second spacing given to you?

Analysis and Discussion

Based on your experimental results, please answer the following questions:

ïWhat gives a falling object its acceleration?

ïAt any given time, all of the nuts should have the same velocity. Why are the time intervals between the evenly spaced nuts different?

To understand this quantitatively, consider the following diagrams that model our string-hex nut systems:

Set d = 10 cm (0.1 m)

Using the kinematic equations, calculate the time it takes for each of the equally-spaced masses in the left diagram to hit the ground. Perform the same calculation for the staggered mass system in the right diagram. How does the time change between impacts of successive masses in both scenarios? Does this agree with your observations?

ïIn the staggered hex nut system that you dropped, which hex nut had the highest velocity when hitting the ground? Calculate this velocity using the proper kinematic equations.

ïSay you have a very long string and want the hex nuts to hit the ground 1 second apart. Using the kinematics equations, determine the spacing for 5 nuts to hit with equal timing. How much string would you need? (Hint: plug in time values starting with t = 1 second into the kinematics equations to find each nut distance.)

Conclusions

References