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Lab Assignment 2: Projectile Motion

Instructor’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:

• • In the first part of the lab, you will launch a marble off of a table or other elevated surface and measuring the horizontal distance that the marble travels. From this distance, you will calculate the launch velocity of the marble. You’ll then repeat the experiment using a different launch height and try to predict the new horizontal distance using the velocity that you derived from the first part of the experiment.

• • In the second part of the lab, you will launch small foam rockets. The first part of this experiment involves measuring the flight time of the rocket and deriving launch speed. In the second part of the experiment, you will explore the dependence of range on launch angle.

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

• • Although you are welcome to use the water and corn starch technique outlined in the eScience lab manual, a slightly less messy technique is suggested. Take a towel and fold it into several layers. Place the towel in the marble landing area and smooth the surface with your hand. When the marble hits the towel, its landing is deadened and you will see a slight impression of where it landed. Measure to this impression to determine the range of the marble. Consider also placing a sheet of aluminum foil on the towel, again to have a noticeable mark for marble strike point.

• • Make sure that you place your marble at the same position on your ramp. This helps insure the repeatability of launch speed.

Rocket experiment

• • The best results occur when you have a consistent squeeze on the launch bulb, firm but not excessively vigorous. The rocket flies more consistently and travels a manageable distance from a measurement perspective.
• • Before collecting data, make sure you practice you launch technique. Try to squeeze the launch bulb in a consistent manner to minimize experimental variation.
• • Launch the rocket close to the ground for your range measurements.

Procedure 1 – marble launch – 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 marble’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
Trial Number	Distance (meters)	Calculated velocity (m/s)
1
2
3
4
5
6
7
8
9
10
Average
Standard Deviation

Procedure 2 – marble launch – 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
Trial Number	Observed Distance (meters)	Predicted Distance (meters)	Difference between observed and predicted distances (meters)
1
2
3
4
5
6
7
8
9
10
Average
Standard Deviation

Procedure 3 – 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 ½ the total time of flight.

Let t = time to reach peak

v = 0 at the peak

v = v₀ – gt

0 = v₀ – 9.8 t

v₀ = 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, ½ the flight time.

Data table for rocket experiment – vertical launch

Trial Number	Flight time (sec)	Calculated velocity (m/s)
1
2
3
4
5
6
7
8
9
10
Average
Standard Deviation

Procedure 4 – 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 (2θ) : where theta (θ) is the launch angle (measured from the horizontal).

Data tables for rocket experiment – angle experiments

Angle = 30 degrees
Trial Number	Predicted range (meters)	Measured range (meters)	Difference (meters)
1
2
3
4
5
Average
Standard Deviation

Angle = 45 degrees
Trial Number	Predicted range (meters)	Measured range (meters)	Difference (meters)
1
2
3
4
5
Average
Standard Deviation

Angle = 60 degrees
Trial Number	Predicted range (meters)	Measured range (meters)	Difference (meters)
1
2
3
4
5
Average
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

• • Suppose you altered your existing ramp so that the marbles had twice their initial velocity right before leaving the ramp. How would this change the total distance traveled and the time that the marbles were in the air?

• • Did your prediction in Procedure 2 come close to the actual spot? Find the percent error of your predicted distance (expected) compared to the actual average distance (observed). What are some sources of error in this experiment?

% error = [ (observed value ‐ expected value)]/ expected value X100

Rocket Experiment

• • Of the three angles that you tested, what angle gave the greatest range? The least?

• • What role does air resistance play in affecting your data?

• • Discuss any additional sources of error, and suggest how these errors might be reduced if you were to redesign the experiment.

Conclusions

References

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