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Projectile Motion EX-9948 Page 1 of 15 Projectile Motion EQUIPMENT 1 Mini Launcher ME-6825 2 Smart Timer ME-8930 1 Time of Flight Accessory ME-6810 3 Photogate Head ME-9498A 1 Photogate Bracket ME-6821 1 Universal Table Clamp ME-9376B 1 Carbon Paper SE-8693 1 Metric Measuring Tape SE-8712A 1 Steel Ball INTRODUCTION The purpose of this experiment is to predict the horizontal range of a projectile shot from various heights and angles. In addition, students will compare the time of flight for projectiles shot horizontally at different muzzle velocities. THEORY The horizontal range, x, for a projectile can be found using the following equation: (1) where v x is the horizontal velocity and t is the time of flight. To find the time of flight, t, the following kinematic equation is needed: (2) Written by Sean McKeever and Geoffrey Clarion

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Page 1: Projectile Motion

Projectile Motion EX-9948 Page 1 of 15

Projectile Motion

EQUIPMENT

1 Mini Launcher ME-68252 Smart Timer ME-89301 Time of Flight Accessory ME-68103 Photogate Head ME-9498A1 Photogate Bracket ME-68211 Universal Table Clamp ME-9376B1 Carbon Paper SE-86931 Metric Measuring Tape SE-8712A1 Steel Ball

INTRODUCTION

The purpose of this experiment is to predict the horizontal range of a projectile shot from various heights and angles. In addition, students will compare the time of flight for projectiles shot horizontally at different muzzle velocities.

THEORY

The horizontal range, x, for a projectile can be found using the following equation:

(1)

where vx is the horizontal velocity and t is the time of flight.

To find the time of flight, t, the following kinematic equation is needed:

(2)

where y is the height, ay is the acceleration due to gravity and vy0 is the vertical component of the initial velocity.

When a projectile is fired horizontally (from a height), the time of flight can be found from rearranging Equation 2. Since the initial velocity is zero, the last term drops out of the equation yielding:

(2a)

Written by Sean McKeever and Geoffrey Clarion

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Projectile Motion EX-9948 Page 2 of 15

When a projectile is fired at an angle and it lands at the same elevation from which it was launched, the first term in Equation 2 is dropped. Rearranging yields:

(2b)

When a projectile is fired from a height, none of the terms drop out and Equation 2 must be rearranged as follows:

(2c)

Equation 2c must be solved quadratically to find the time of flight, t.

Written by Sean McKeever and Geoffrey Clarion

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EXPERIMENT SETUP – Part A1: Muzzle Velocity

1. Choose one corner of a table to place the projectile launcher. Make sure a distance of about 3 meters is clear on the floor around the table.

2. Clamp the launcher to the corner of the table using the Universal Table Clamp (see photo below).

3. Using the attached plumb bob, adjust the angle of the launcher to 0o.

4. Slide the Photogate Bracket into the groove on the bottom of the launcher and tighten the thumbscrew.

5. Connect two photogates to the bracket (see photo below).

Written by Sean McKeever and Geoffrey Clarion

SafetyWear Safety Goggles. Do not place foreign objects into the Launcher. Do not look into the Launcher. Do not aim the Launcher at others.

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6. Plug the photogate closest to the launcher into port 1 on the Smart Timer. Plug the other photogate into port 2.

7. Turn on the Smart Timer. Using the red "Select Measurement" button, choose the "Time" Measurement."

8. Using the blue "Select Mode" button, choose the "Two Gates Mode." This will measure the

time it takes the projectile to travel between the two photogates.

PROCEDURE – Part A1: Muzzle Velocity

1. Using the cross-hairs on the side, record the height of the projectile. In addition, record the spacing between the two photogates.

2. Place the steel ball into the launcher and use the push rod to load the ball until the “3rd click” is heard.

3. Hold a piece of cardboard a few centimeters past the 2nd photogate to block the ball.

4. Press the Start button on the Smart Timer.

5. Pull the launch cord on the launcher.

6. Record the time from the Smart Timer display.

7. Repeat steps 2-6 for 2 clicks and 1 click.

Data Table A1Projectile Height: _________ mPhotogate Spacing: ________________ mNumber of Clicks Time Between Photogates (s)

3rd Click2nd Click1st Click

Written by Sean McKeever and Geoffrey Clarion

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PROCEDURE - Part A2: Muzzle Velocity v. Time of Flight

1. Remove the photogate from port 2 of the Smart Timer and replace it with the Time of Flight Accessory.

2. Load the ball into the launcher to the 3rd click.

3. Predict where the ball will land and explain your prediction.

4. Launch the ball and note where it lands. Place the Time of Flight Accessory such that the ball will land on it.

5. Place the steel ball into the launcher and use the loader to push the ball in until the “3rd click” is heard.

6. Press the Start button on the Smart Timer. Note: Use the same Smart Timer setting as Part A1.

7. Pull the launch cord on the launcher.

8. Record the time from the Smart Timer display into Data Analysis Table A2.

9. Repeat steps 2-8 for 2 clicks and 1 click.

DATA ANALYSIS – Part A2: Muzzle Velocity v. Time of Flight

1. Use the time between the photogates and the spacing between the photogates to find the muzzle velocity of the projectile for each firing.

2. Record these values into Data Analysis Table A2.

Written by Sean McKeever and Geoffrey Clarion

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Data Analysis Table A2Number of Clicks Muzzle Velocity (m/s) Time of Flight (s)

3rd Click2nd Click1st Click

PREDICTION - Part B: RANGE

1. Using the initial height of the projectile and the muzzle velocity from the "3rd click," calculate the theoretical horizontal range of the ball.

EXPERIMENT SETUP – Part B: RANGE

1. Tape a target to the floor in front of the projectile launcher at a distance equal to the range prediction calculated above.

2. Place carbon paper over the target.

3. Align the projectile launcher.

4. Launch the ball from the 3rd click. Repeat four more times.

5. Remove the carbon paper. Observe the locations where the ball struck the Bull's Eye.

PARTS A and B: CONCLUSIONS/QUESTIONS

1. Draw a force diagram for the ball as it flies through the air.

2. Which variable(s) affect the horizontal range?

3. How would the horizontal range change if the muzzle velocity was doubled? Explain how.

4. How would the horizontal range change if the height from the ground was quadrupled? Explain how.

5. How would the horizontal range change if the mass of the ball was doubled? Explain how.

6. Which variable(s) affect the time of flight?

7. How would the time of flight change if the muzzle velocity was doubled? Explain how.

8. How would the time of flight change if the height from the ground was quadrupled? Explain how.

9. How would the time of flight change if the mass of the ball was doubled? Explain how.

Written by Sean McKeever and Geoffrey Clarion

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10. What force are we able to ignore in this experiment? Explain.

EXPERIMENT SETUP PART C - LAUNCHING AT AN ANGLE

1. Clamp the launcher to the edge of a table using the Universal Table Clamp so that the ball launches from and lands at the same elevation (see photo below).

2. Adjust the angle of the launcher to 10o. Note: With the photogate bracket and photogates attached to the launcher, the lowest angle is approximately 23o.

3. Plug the photogate closest to the launcher into port 1 on the Smart Timer. Plug the other photogate into port 2.

4. Turn on the Smart Timer. Using the red "Select Measurement" button, choose the "Time" Measurement."

5. Using the blue "Select Mode" button, choose the "Two Gates Mode." This will measure the time it takes the projectile to travel between the two photogates.

PROCEDURE PART C - LAUNCHING AT AN ANGLE

1. Using the push rod, push the ball as far as possible into the Launcher. Make sure three clicks are heard. Using the string, pull back on the trigger. Note the location on the table where the ball lands.

2. Tape a sheet of blank paper at this location. Place carbon paper over the blank paper.

3. Load the Launcher.

4. Press the Start button on the Smart Timer.

5. Launch the ball.

6. Use the tape measure to find the horizontal range.

7. Record the experimental data. Enter the value of the angle in degrees, the time between photogates, and the horizontal range in meters into the “Measured Range” data table.

8. Repeat the steps 1-7 for 20, 30, 40, 50, 60, 70 degrees.

Written by Sean McKeever and Geoffrey Clarion

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Data Table: C1 Measured RangeDistance Between Photogates: __________ m

Angle(degrees)

Time between Photogates (s)

Horizontal Range (m)

10203040506070

ANALYSIS PART C - LAUNCHING AT AN ANGLE

1. Using the distance between the photogates and the time between the photogates (Data Table C1), calculate the initial velocities of the ball. Record these values into the Initial Velocity Analysis Table.

Analysis Table C2: Initial VelocityAngle (degrees) Initial Velocity (m/s)

10203040506070

2. Using the initial velocity and the angle; calculate the horizontal range in meters. Enter this value for each angle into the “Calculated Range” Analysis Table. Hint: Calculate the components of the initial velocities. See the “THEORY” section.

Analysis Table C3: Calculated Range

Angle (degrees) Horizontal Range (m)10203040506070

Written by Sean McKeever and Geoffrey Clarion

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3. Use DataStudio to plot both the Measured Horizontal Range vs. Angle and the Calculated Horizontal Range vs. Angle on the same graph.

CHALLENGE PART C - LAUNCHING AT AN ANGLE

Show your Range vs. Angle graph to the teacher. The teacher will place the Bull's Eye at a particular position on the table. Measure the horizontal distance to the center of the Bull's Eye. Place the carbon paper on top of the Bull's Eye. The objective is to hit the center. You will have 5 attempts. The launcher may be adjusted between attempts. PART C: CONCLUSIONS/QUESTIONS

1. Sketch the trajectory of your projectile when it was shot at an angle of 25o. Draw 5 qualitative horizontal velocity vectors at different locations on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the velocities. In other words, low velocities should be represented by short arrows and long arrows should represent large velocities.

2. Draw 5 qualitative vertical velocity vectors at the same points on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the velocities.

3. Draw another sketch of the trajectory of your projectile when it was shot at 25 degrees. Draw 5 qualitative horizontal acceleration vectors at different locations on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the accelerations.

4. Draw 5 qualitative vertical acceleration vectors at the same points on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the accelerations.

5. Draw a force diagram of the ball as it rests in the Launcher. Draw a force diagram of the ball as it flies through the air.

6. Refer to your Angle vs. Range graph. What angle corresponds to the maximum range? Explain why this particular angle produces the maximum range.

7. In general terms, at what angle is the Launcher the most precise? Explain.

Written by Sean McKeever and Geoffrey Clarion

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EXPERIMENT SETUP PART D - LAUNCHING AT AN ANGLE FROM A HEIGHT

1. Clamp the launcher to the edge of a table using the Universal Table Clamp so that the ball launches from a position above where it will land (see photo above).

2. Adjust the angle of the launcher to -20o.

3. Plug the photogate closest to the launcher into port 1 on the Smart Timer. Plug the other photogate into port 2.

4. Turn on the Smart Timer. Using the red "Select Measurement" button, choose the "Time" Measurement."

5. Using the blue "Select Mode" button, choose the "Two Gates Mode." This will measure the time it takes the projectile to travel between the two photogates.

PROCEDURE PART D - LAUNCHING AT AN ANGLE FROM A HEIGHT

1. Using the cross hairs on the side of the launcher, measure and record the height of the ball's starting point.

2. Using the plunger, push the ball as far as possible into the Launcher. Make sure three clicks are heard. Using the string, pull back on the trigger. Keep track of the location on the floor where the ball lands.

3. Tape a sheet of blank paper at this location. Place carbon paper over the blank paper.

4. Load the Launcher.

5. Press the Start button on the Smart Timer.

6. Launch the ball.

7. Use the tape measure to find the horizontal range.

8. Record the experimental data. Enter the value of the angle in degrees, the time between photogates, and the horizontal range in meters into the “Measured Range” data table.

Written by Sean McKeever and Geoffrey Clarion

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9. Repeat the steps 1-8 for the angles listed below in Data Table D1.

Data Table D1: Measured RangeHeight: ________________________ mDistance Between Photogates: ______ m

Angle(degrees)

Time between Photogates (s)

Horizontal Range (m)

-20-15-10-5051015202530354045505560657075

Written by Sean McKeever and Geoffrey Clarion

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ANALYSIS PART D - LAUNCHING AT AN ANGLE FROM A HEIGHT

1. Using the distance between the photogates and the time between the photogates (Data Table D1), calculate the initial velocities of the ball. Record these values into the Initial Velocity Analysis Table.

Analysis Table D2: Initial VelocityAngle (degrees) Initial Velocity (m/s)

-20-15-10-5051015202530354045505560657075

2. Using the initial velocity and the angle; calculate the horizontal range in meters. Enter this value and the angle into the “Calculated Range” Analysis Table. Hint: Find the vertical component of the initial velocity and the initial height of the projectile. Use these values in equation 2c and solve it quadratically to find the time of flight.

Written by Sean McKeever and Geoffrey Clarion

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Analysis Table D3: Calculated RangeAngle

(degrees)Horizontal Range (m)

-20-15-10-5051015202530354045505560657075

Using DataStudio software, plot both the Measured Horizontal Range vs. Angle and the Calculated Horizontal Range vs. Angle on the same graph.

PART D: CONCLUSIONS/QUESTIONS

1. Sketch the trajectory of your projectile when it was shot at an angle of 60 degrees. Draw 5 qualitative horizontal velocity vectors at different locations on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the velocities. In other words, low velocities should be represented by short arrows and long arrows should represent large velocities.

2. Draw 5 qualitative vertical velocity vectors at the same points on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the velocities.

3. Draw another sketch of the trajectory of your projectile when it was shot at 60 degrees. Draw 5 qualitative horizontal acceleration vectors at different locations on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the accelerations.

4. Draw 5 qualitative vertical acceleration vectors at the same points on your sketch. Make sure the lengths of the vectors represent the relative magnitudes of the accelerations.

Written by Sean McKeever and Geoffrey Clarion

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5. Draw a force diagram of the ball as it rests in the Launcher. Draw a force diagram of the ball as it flies through the air.

6. Imagine two balls at the same height. At the same instant, one is dropped and the other is fired horizontally. Which ball would hit the ground first? Use the force diagrams and vectors drawn above to explain your answers.

7. Refer to your Angle vs. Range graph. What angle corresponds to the maximum range? Explain why this particular angle produces the maximum range.

8. In general terms, at what angle is the Launcher the most precise? Explain.

Written by Sean McKeever and Geoffrey Clarion

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PREFACE TASK

1. Draw projection track of projectile motion along with projection component that work at any high?

2. Mention of components which work in projectile motion?3. Write formulas contained in projectile motion?

Written by Sean McKeever and Geoffrey Clarion