Lab
Projectiles Released at an Angle
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When projectiles are released at an angle, their trajectory has unique horizontal and vertical behaviors. Vertically, gravity still pulls unilaterally and results in a uniform downward acceleration of -9.8 m/sec
^{2}
; while horizontally, in the absence of air resistance, the projectile maintains a constant velocity.
In this experiment we are going to use a projectile launcher to vary the angle of release for a piece of wooden dowel. The launcher employs a compressed spring to provide the initial launch force and a protractor to measure the angle of release.
When you go outside, you will work in teams of four. One person will be responsible for launching the dowel. The next two team members will be responsible for observing the dowel's trajectory and marking its impact position. The final member will measure and record the dowel's range. The dowel will be launched three times at 5 different angles: 15º, 30º, 45º, 60º, and 75º and its subsequent range recorded.
Each team will be supplied with one c-clamp, one launcher, one dowel, one washer "on a string," and five meter sticks.
Part I
Before you can start changing the projectile's angle of release, you need to first calibrate the launcher. This is done by launching the dowel horizontally from the top of a table and measuring its range along with the table's height. With that data, you will be able to calculate the launcher's "muzzle velocity." The magnitude of this velocity will remain constant throughout the rest of the experiment. Make sure that you ALWAYS compress the spring to the same slit on the PVC tube.
Refer to the following information for the next five questions.
In the blanks provided below, record the requested data and calculations for your "horizontal" launch. Be sure to record the range for each of your three trials on your papers to support your average.
What is the number of your launcher (1-8)?
(a) height of the table (in meters)
(b) average range of the dowel (in meters) for three releases
(c) time the dowel spent in the air (in seconds)
(d) muzzle velocity of the launcher (in m/sec)
Part II
Now you will investigate the relationship between the angle of release and the dowel's range. For this phase of the experiment you will have a net vertical displacement of zero - that is, you will place the launcher on the ground not on the table. For each angle, measure and record the range for three trials.
angle
trial 1
trial 2
trial 3
average
15º
30º
45º
60º
75º
Part III
In the final part of this experiment you will launch a dowel from the second floor catwalk. This time you will only launch at two angles - 30º and 45º. Once again, you will launch three trials for each angle.
What was the height of the balcony (in meters)?
angle
trial 1
trial 2
trial 3
average
Conclusions
The first analysis that you need to complete is the graph 1-ProjectileLauncher with your data from Part II. What was the slope of your graph?
What was the R
^{2}
value for your graph?
On this graph, your numerical slope equals v
^{2}
/g. Using this fact, calculate your launcher's muzzle velocity.
Calculate a percent difference between the value for your launcher's muzzle velocity from Part I and your previous answer.
Theoretically, complementary angles should have the same range. Which of your two sets of complementary angles had closer values?
15º and 75º
30º and 60º
Why do you think that the other set of complementary angles were not closer in value?
Using your experimental average range for 45º, calculate the launch velocity of your launcher. Show all of your calculations in an H|V chart.
Calculate a percent difference between the value for your launcher's muzzle velocity from Part I and your previous answer for 45º.
When you launched from the balcony, which angle achieved the greater range?
30º
45º
60º
Did the angle achieving the greater range change from when you launched from the ground?
yes
no
After examining the diagram shown below, determine the required value for each question. Let the launch velocity, V, equal your value found in Part I. The black trajectory represents a 45º angle of launch; while the red trajectory represents a 30º angle of launch. You may use energy methods to find velocities and heights, but you must use kinematics to determine time and range. Show ALL of your calculations on your lab report.
What is the height of point A?
What is the speed and direction of the projectile at point A?
What is the height of point B?
What is the speed and direction of the projectile at point B?
What is the range of point C?
What is the speed and direction of the projectile at point C?
What is the range of point D?
What is the speed and direction of the projectile at point D?
How much time did it take to reach E?
What is the range of point E?
How much time did it take to reach F?
What is the range of point F?
How fast were both projectiles travelling at the instant that they impacted the ground?
At what angle did the projectile impact the ground at point E?
At what angle did the projectile impact the ground at point F?
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