Download Lab 8

Astronomy 102
Name:
Lab 8: Measuring the acceleration of a rocket
Objective: To measure the acceleration of a rocket through video image analysis
and to calculate the rocket’s thrust.
Needed: 2-liter bottle, water, pump, rocket launcher, two-meter (or longer) stick,
high-speed camera, analysis software
1. To figure out the thrust of your 2-liter water bottle rocket, we cannot do a
similar analysis as you did for the balloon. In other words, we can’t simply use the
rocket equation. Why not? Hint: consider what’s different about the direction of
the water bottle rocket compared to the balloon, and what force might need to be
considered.
Instead, we are going to use Newton’s 2nd law, famously F = m a, where F is the
force on the rocket, m is the mass of the rocket and a is the acceleration. Clearly,
the mass of the rocket will be a relatively easy thing to measure, but what is
acceleration? Acceleration is defined as how much faster (or slower) something
moves than it did before. More formally, it is the change in velocity divided by the
time duration in which the change takes place.
2. Set up the water bottle rocket, as per instructor directions, place the measuring
stick (ideally with easily-visible markings) next to the launcher and use the
camera to record the first few seconds of the launch. Measure the initial mass of
the rocket (in kg) and record it below.
Ideally, the camera will be set to take multiple exposures per second, and the
rocket will be captured in the images during that duration. Launch the rocket.
3. Using the software provided (or by going frame by frame through the camera’s
images), determine the time after launch (in seconds) and the height of the
rocket (in meters) at each time. I find using the top of the bottle the easiest to
see in most images. Write those observations in the table below:
Time
after
launch
(s)
Height of
rocket
flight (m)
Time
duration
(s)
Difference
in height
(m)
Speed
during
interval
(m/s)
Change
in speed
(m/s)
Acceleration
(m/s2)
4. The time duration is simply the difference in time (in seconds) between
images, and should be the same between any adjacent pair of images. The
difference in height between adjacent images is similarly calculated; it should
not be the same between different pairs of adjacent images. The speed during
the interval is the difference in height divided by the time duration. Enter all
these calculation results into the table.
5. The change in speed is the difference between an adjacent pair of the “speed
during interval” entries. The acceleration is therefore the change in speed
divided by the time duration. Enter these calculation results into the table.
6. The acceleration sure has odd units – m/s2. Explain, either by words or by
symbols, how acceleration ended up with these units.
7. The acceleration due to gravity at the Earth’s surface is 9.8 m/s2. This number
is often referred to as “g”. What percent of g is your rocket’s acceleration? Show
your calculation.
8. The force on the rocket is its mass times its acceleration. For which time
interval will the rocket’s acceleration be most accurate and why? Hint: when was
the value of the mass of the rocket you wrote down most accurate?
9. Calculate the force on the rocket; the answer will be in Newtons (N).
10. Finally, what is the thrust of your rocket in Newtons? This isn’t the same
answer as in question 9, because your rocket is also overcoming the force of gravity.
Calculate the force of gravity acting on the rocket initially, then add those Newtons
to the answer to question 9 to get the thrust. Show your calculation! How does your
rocket’s thrust compare to the thrust of a B6-4 model rocket engine?