To determine the trajectory of a model rocket.
Equipment
PASCO Rocket Engine Test Bracket, dual range force probe, iron ring stand, Estes B6 or C6 motor, Logger Pro
Procedure
After setting up the model rocket engine on a stable platform, open logger pro.
Select EXPERIMENT, then DATA COLLECTION.
Set duration to 3 seconds.
Set sampling rate to 1000 samples/second.
Click the TRIGGERING tab.
Select triggering.
Select decreasing.
Set trigger force to -0.2 Newtons
BE SURE TO CLEAR THE AREA AROUND THE EXPERIMENTAL SET UP!
Set the zero force probe.
Click the collect data icon (you should observe "waiting for trigger and data..." within the top portion of the graph area)
Once the area is clear, ignite the motor
After the motor has stopped. You should be able to see a graph of force vs time. From the graph, make your assumptions on a few questions.
The questions are as follows:
1. Draw a system schema and force diagram and apply Newton's Second Law to a rocket on the launch pad.
2. Redraw the system schema and force diagram and a statement of Newton's Second Law based on this force diagram for the moment the rocket leaves the ground.
a. What agent is causing the upward force?
b. Do you think the thrust force is constant? Explain.
3. As the fuel burns, is your rocket speeding up or slowing down? Which force has to be bigger for this to occur? Do you need to modify your force diagram?
4. Your rocket is not a particle. Do you think you have to deal with air resistance? Redo your system schema, force diagram, and statement of Newton's Second Law to include it.
5. Do you think F(air) is constant? If not. what does it depend on?
6. When the rocket has run out of fuel, what direction is still going? Is it speeding up or slowing down? Based on this, what does your force diagram look like now? What is your new statement of Newton's Second Law?
7. How will you know when the rocket reaches its highest point?
8. Get your answers on your boards.
We will use the ideas the class has developed to make a model to figure out how high a real rocket actually goes. We will test your model against experimental data.
9. What specific information and measurements do we need? Be sure to distinguish what quantities need to be looked up and what needs to be measured to do the calculations for your model.
10. Now you will need to obtain the thrust vs time data for a rocket motor. Ultimately, this data will be used to help calculate the height of the rocket flight. Not all of the data that you obtain will be useful for the calculations in your model. Think carefully about which data to include. Consider this: Does the rocket accelerate instantaneously or does the thrust take time to build?
Once you have answered all the questions and collected your experimental data, it is time to launch a real rocket. For this lab, the measurements needed for the maximum height include: mass = 0.0632 kg, diameter = 0.02441 m, delta t = 0.001 s, F(g) = 0.6194, rho = 1.2.
Create an excel spreadsheet with the columns: time (s), F(thrust)(N), a (m/s/s), v (m/s), rhoAv^2 (N), delta r (m), r (m). Set up the spreadsheet with these formulas: a = ( F(thrust) - F(g) - rhoAv^2) / mass , v(final) = v(initial) + a(delta t) , delta r = (v(final)^2 - v(initial)^2) / 2a
Once you have the spreadsheet set up, go to your experimental data table and select the times in which the thrust force is greater than the force of gravity of the rocket (which is 0.6194 N). Select as much time as needed along with the corresponding thrust values. Include the values where thrust is less than gravity at this point. Put those values in the excel spreadsheet. Add the desired constants and make the excel formula based on the written formulas above. Be sure to add the $ symbol before the letter and number of the cell with a constant value. Your table should look like this:
At first, the height values are very small, but this is fine because this happens in the first few seconds of flight. Once more time and thrust values are added, there is a significant change in height. This is where the maximum height can be found. The next two pictures show the maximum height.
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