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Lab Assignment 2: Projectile Motion
Instructorâ€™s Overview
Projectile motion is a part of our everyday experience. When you strike a baseball or softball, you are creating a projectile motion scenario. Similarly, you yourself are a projectile when you jump into a pool to cool off on a sweltering summer day. In this lab you will get some hands-on experience with projectile motion and apply the two-dimensional kinematic equations that we have developed. You will perform experiments and compare your results to theory.
This activity is based on Lab 7 of the eScience Lab kit. Although you should read all of the content in Lab 7, we will be performing a targeted subset of the eScience experiments.
Our lab consists of two main components. These components are described in detail in the eScience manual (pages 83-88). Here is a quick overview:
Note: In the rocket experiment, perform and document steps 1-7. Then launch your rocket at three angles: 30 degrees, 45 degrees, and 60 degrees. Record all of your data in the tables that are provided in this document. Don’t use the tables in the eScience manual.
Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations.
Experiment Tips:
Marble on a ramp
Rocket experiment
Procedure 1 â€“ marble launch â€“ calculating horizontal velocity
In this experiment you will measure the height the marble will fall, that is, the height of the table. From this height you will calculate the time the marble falls, this is the same amount of time the marble will be in flight when launched horizontally off the table. The horizontal component of the marbleâ€™s motion does not affect the time of flight. The marble both moves horizontally and vertically but the time is only dependent on the vertical fall. Note: we are assuming the air does not affect the flight as it would if the object had a wing like structure.
Height of table (y) __________
t =
Calculated time of drop __________
Using a plumb line dropped from the edge of the table make a mark on the floor directly under the edge of the table. (suggest placing the mark on a piece of masking or painters tape on the floor or laying down a piece of paper that is weighted down).
Suggest having a lab partner assist if available. Roll the marble down the ramp and measure the distance the marble traveled horizontally (x). This is the distance from the mark below the table edge to the impact mark. Using this distance and the calculated time of flight calculate the horizontal velocity
v =
Perform 10 trials and record the results in the table below.
Data Table for Marble Procedure 1.
Height = __meters |
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Trial Number |
Distance (meters) |
Calculated velocity (m/s) |
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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Average |
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Standard Deviation |
Procedure 2 â€“ marble launch â€“ predicting range
In this experiment you will increase the height of the table, or you can put the launch ramp on some books. Keep the length of the launching ramp the same to keep the horizontal velocity the same but we want the marble to be in the air longer.
Height of table (y) __________
t =
Calculated time of drop __________
Using the new time of flight and the average horizontal velocity from the table above calculate a predicted horizontal distance. Roll the marble and again measure the horizontal distance as done before. Compare the actual distance with the predicted distance. Repeat for 10 trials and record in the table below.
Data table for marble experiment (Procedure 2):
Height = __meters |
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Trial Number |
Observed Distance (meters) |
Predicted Distance (meters) |
Difference between observed and predicted distances (meters) |
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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Average |
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Standard Deviation |
Procedure 3 â€“ Rocket Launch, determining launch velocity.
In this experiment you will launch a rocket vertically, straight up, and measure the time of flight. We can use either the time to reach the peak of flight or the total time of flight. Measuring the total time of flight is recommended as a longer time is less affected by reaction times in operating the stop watch.
The time to reach the peak is Â½ the total time of flight.
Let t = time to reach peak
v = 0 at the peak
v = v_{0} â€“ gt
0 = v_{0} â€“ 9.8 t
v_{0} = 9.8 t
Perform 10 trials, measure the flight time, and calculate the initial velocity. Remember the equation above uses the time to peak of flight, Â½ the flight time.
Data table for rocket experiment – vertical launch
Trial Number |
Flight time (sec) |
Calculated velocity (m/s) |
1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
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Average |
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Standard Deviation |
Procedure 4 â€“ Rocket Launch at Angles
Using a protractor set the rocket to launch at angles of 30^{o},45^{o}, and 60^{o}.
You will use the range equation to predict the horizontal distance the rocket travels.
R = ()^{2} sin (2Î¸) : where theta (Î¸) is the launch angle (measured from the horizontal).
Data tables for rocket experiment – angle experiments
Angle = 30 degrees |
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Trial Number |
Predicted range (meters) |
Measured range (meters) |
Difference (meters) |
1 |
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2 |
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3 |
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4 |
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5 |
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Average |
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Standard Deviation |
Angle = 45 degrees |
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Trial Number |
Predicted range (meters) |
Measured range (meters) |
Difference (meters) |
1 |
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2 |
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3 |
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4 |
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5 |
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Average |
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Standard Deviation |
Angle = 60 degrees |
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Trial Number |
Predicted range (meters) |
Measured range (meters) |
Difference (meters) |
1 |
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2 |
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3 |
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4 |
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5 |
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Average |
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Standard Deviation |
Analysis and Discussion
Marble experiment calculations
Show your calculation of the launch velocity of the marble as a function of height and distance travelled:
Use your equation above to solve for the range as a function of launch velocity and height):
Rocket calculations
Show your calculation of the launch velocity of the rocket as a function of flight time.
Show your calculations of predicted range for the three angles used.
Based on your experimental results, please answer the following questions:
Marble Experiment
% error = [ (observed value â€ expected value)]/ expected value X100
Rocket Experiment
Conclusions
References
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