Excellent job! Calculations done correctly and work shown. Care must have been taken into taking data because % errors are relatively low with the causes of error that are unavoidable.
20/20
Purpose: Calculate the velocity of the projectile launcher.
Investigate the various angles of launch and the corresponding range.
Materials: projectile launcher projectiles meter stick clamp
SAFETY: Only launch projectile in one direction of the room.
Never look down the barrel of your projectile launcher.
Never aim or fire your projectile launcher at anyone.
Operation: While pushing the wooden peg projectile into the launcher, slide the washer into the first slot (closest to
the edge of the PVC tube). Slide the washer into the slot just a bit (a few millimeters). If the washer is pushed in too far, you will have trouble releasing the projectile. To release the projectile, pull on the string quickly in a direction perpendicular to the tube so that the washer slides out.
Procedure: Part I:
Clamp the wooden base of the projectile launcher onto the edge of your lab table. Align your launcher horizontally (0°). Measure the height of the launcher tube (to the ground). Fire the projectile three times and record the average horizontal distance.
Part II:
Place your launcher on the floor. The person performing the launch should step on the wooden base with one foot to keep it stable. Fire the projectile at 10°, 20°, 30°, 40°, 50°, and 60° above the horizontal. Do NOT fire anything above this last angle or you run the risk of hitting the ceiling. Record the range for each fire and place into the data table on the back page.
Calculations: Refer to your notes or previous problems done in class to guide you.
1. Determine the horizontal launch velocity of your launcher.
3. Predict the time of flight, maximum height, and range of your angled launches (assuming that the
launch velocity is the same as in Part I of your lab). Remember to break down your launch velocity into
its x and y components. Compare your predicted range to the recorded range by calculating the % error. Show your work for just one of the six trials.
1. Describe the horizontal velocity of your projectile and any changes it encounters.
The horizontal velocity of the projectile decreases as the angle of launch increases from 0 degrees to 60 degrees. It remains constant during the flight of the projectile, however. This is because there is no acceleration in the horizontal direction as gravity does not act horizontally.
2. If you were to triple the speed of a projectile fired horizontally, how would the range change?
If the speed of a fired projectile is tripled, its range will also triple. This is because velocity and distance have a direct relationship, as can be seen in the function vx = Δx/Δt, or Δx = vx(Δt).
3. Describe the vertical velocity of your projectile and any changes it encounters.
The vertical velocity of the projectile decreases towards zero as it ascends towards the apex of it flight. It then becomes negative and continues to decrease as it returns towards the ground.
4. Do you see any pattern(s) in your angle of launch vs. range data table? Explain your observations.
Range increased as the angle of launch was increased from 10 degrees to 50 degrees. It then began to decrease at 60 degrees. The ranges for angles of launch that are complementary to one another are very similar. This suggests that the angle of launch with maximum range is around 45 degrees. If the tests had been conducted at intervals of 5 degrees instead of 10 degrees, we probably would have seen that the largest range came at an angle of launch of 45 degrees.
5. Identify potential causes of experimental error.
One cause of error was an inexact firing system that may have caused each projectile to have a different initial velocity. Another was that there was no way to be exact on where the projectiles actually landed, leading to inexact range data. Furthermore, the formulas used to determine velocity, time, height, and range all assume air resistance. As the tests were not conducted in a vacuum, any air resistance may have skewed the data.
20/20
Purpose: Calculate the velocity of the projectile launcher.
Investigate the various angles of launch and the corresponding range.
Materials: projectile launcher projectiles meter stick clamp
SAFETY: Only launch projectile in one direction of the room.
Never look down the barrel of your projectile launcher.
Never aim or fire your projectile launcher at anyone.
Operation: While pushing the wooden peg projectile into the launcher, slide the washer into the first slot (closest to
the edge of the PVC tube). Slide the washer into the slot just a bit (a few millimeters). If the washer is pushed in too far, you will have trouble releasing the projectile. To release the projectile, pull on the string quickly in a direction perpendicular to the tube so that the washer slides out.
Procedure: Part I:
Clamp the wooden base of the projectile launcher onto the edge of your lab table. Align your launcher horizontally (0°). Measure the height of the launcher tube (to the ground). Fire the projectile three times and record the average horizontal distance.
Height of Launcher: 0.94 (m)
Horizontal Distance Trial 1: 3.43 (m)
Horizontal Distance Trial 2: 3.15 (m)
Horizontal Distance Trial 3: 3.12 (m) Avg. Horizontal Distance: 3.23 (m)
Part II:
Place your launcher on the floor. The person performing the launch should step on the wooden base with one foot to keep it stable. Fire the projectile at 10°, 20°, 30°, 40°, 50°, and 60° above the horizontal. Do NOT fire anything above this last angle or you run the risk of hitting the ceiling. Record the range for each fire and place into the data table on the back page.
Calculations: Refer to your notes or previous problems done in class to guide you.
1. Determine the horizontal launch velocity of your launcher.
viy = 0m/s
vx = ?
Δy = -9.4m
Δx = 3.23m
ay = -9.8m/s^2
Δt = ?
yf = yi + viy(t) + 0.5(ay)(t^2)
-0.94m = 0m + 0m/s(t) + 0.5(-9.8m/s^2)(t^2)
-0.94 = -19.6m/s^2(t^2)
t^2 = 0.19
Δt = 0.44sec
vx = Δx/Δt
vx = 3.23m/0.44sec
vx = 7.3m/s
2. Determine the vertical velocity of the projectile just as it is about to hit the ground.
viy = 0m/s
vx = ? = 7.3m/s
Δy = -9.4m
Δx = 3.23m
ay = -9.8m/s^2
Δt = ? = 0.44sec
ay = (vfy - viy)/Δt
-9.8m/s^2 = (vfy - 0m/s)/0.44sec
vfy = -4.31m/s
3. Predict the time of flight, maximum height, and range of your angled launches (assuming that the
launch velocity is the same as in Part I of your lab). Remember to break down your launch velocity into
its x and y components. Compare your predicted range to the recorded range by calculating the % error. Show your work for just one of the six trials.
10 Degree Launch Trial
vi = 7.3m/s
vx = ? = 7.19m/s
viy = ? = 1.27m/s
vfy (at peak) = 0m/s
ay = -9.8m/s^2
Δy = ? = 0.08m
Δx = ?
Δt = ? = 0.26sec
vx = 7.3cos10degrees = 7.19m/s
viy = 7.3sin10degrees = 1.27m/s
vfy^2 = viy^2 + 2(ay)(Δy)
(0m/s)^2 = (1.27m/s)^2 + 2(-9.8m/s^2)(Δy)
0 = 1.61 - 19.6Δy
19.6Δy = 1.61
Δy = 0.08m
ay = (vfy - viy)/Δt
-9.8m/s^2 = (-1.27ms - 1.27m/s)/Δt
-9.8 = -2.54/Δt
Δt = 0.26sec
vx = Δx/Δt
7.19m/s = Δx/0.26sec
Δx = 1.87m
% Error = | (Known - Experimental) / Known | * 100
% Error = | (1.84m - 1.87m) / 1.84m | * 100
% Error = | -0.03 / 1.84 | * 100
% Error = 1.6%
Questions:
1. Describe the horizontal velocity of your projectile and any changes it encounters.
The horizontal velocity of the projectile decreases as the angle of launch increases from 0 degrees to 60 degrees. It remains constant during the flight of the projectile, however. This is because there is no acceleration in the horizontal direction as gravity does not act horizontally.
2. If you were to triple the speed of a projectile fired horizontally, how would the range change?
If the speed of a fired projectile is tripled, its range will also triple. This is because velocity and distance have a direct relationship, as can be seen in the function vx = Δx/Δt, or Δx = vx(Δt).
3. Describe the vertical velocity of your projectile and any changes it encounters.
The vertical velocity of the projectile decreases towards zero as it ascends towards the apex of it flight. It then becomes negative and continues to decrease as it returns towards the ground.
4. Do you see any pattern(s) in your angle of launch vs. range data table? Explain your observations.
Range increased as the angle of launch was increased from 10 degrees to 50 degrees. It then began to decrease at 60 degrees. The ranges for angles of launch that are complementary to one another are very similar. This suggests that the angle of launch with maximum range is around 45 degrees. If the tests had been conducted at intervals of 5 degrees instead of 10 degrees, we probably would have seen that the largest range came at an angle of launch of 45 degrees.
5. Identify potential causes of experimental error.
One cause of error was an inexact firing system that may have caused each projectile to have a different initial velocity. Another was that there was no way to be exact on where the projectiles actually landed, leading to inexact range data. Furthermore, the formulas used to determine velocity, time, height, and range all assume air resistance. As the tests were not conducted in a vacuum, any air resistance may have skewed the data.