Laboratory: Nerf Cannon Lab (Video)



Laboratory: Measurement & Video Analysis of a Nerf Gun Projectile

Purpose:

1. To study the motion of a freely falling object.

2. To determine the maximum height and muzzle velocity of a projectile shot from a Nerf Cannon

Introduction: General Otto von Nerf has developed the ultimate weapon of mass destruction, the Nerf Blaster cannon. You have been assigned the task of determining the vital operating characteristics of this lethal device, namely the muzzle velocity and maximum height of a launched projectile.

Using the laws of kinematics you will analyze this device. First, the change in (vertical) velocity/speed of an object under constant acceleration can be determined by the relationship:

Δv = vfinal - vinitial = at

Since the acceleration on the object while it is in flight is strictly due to gravity (neglecting air resistance), the equation can be re-written as:

Δv = vfinal - vinitial = - gt (or -gthang)

where g is 10 m/s2 (downward) and t is the hang time (or thang) of the launched ball. In this equation, vinitial is the muzzle velocity (vmuzzle) of a projectile launched from the cannon. It should be noted that since air resistance will not be considered, it can be assumed that the magnitude of the speed of the object at the end of its flight (i.e. the bottom of its trajectory) is the same as the muzzle velocity. Also, as the projectile comes down it is moving in the opposite direction as when it was shot up, thus we can say:

vfinal = - vinitial = - vmuzzle

Thus, we can re-write our motion equation for the muzzle velocity as:

Δv = - vmuzzle - vmuzzle = - gthang

or,

Equation 1: vmuzzle = ½ . gthang

This equation will be utilized to determine the muzzle velocity of a projectile launched from the Nerf Blaster.

To determine the maximum height of a launched projectile, a separate kinematic equation will be utilized. The distance traveled by an object under constant acceleration is given by the relationship:

Equation 2: d = ½ gt2

This equation relates the distance traveled by an object projected from the cannon to the time the object is in flight. Since we are interested in the height of the projectile’s trajectory, the time, t, in this equation refers to the time elapsed for the ball to reach its highest point. In other words, t is half of the hang time of the launched ball, or

t = ½thang

We will use this relationship to determine the maximum height of a projectile shot vertically from a Nerf cannon.

Preliminary Questions:

1) For a freely falling object, what is the acceleration (ignore air resistance)?

2) Consider a ball shot directly upward into the air (free fall) from ground level.

a) How does the time on the way up compare to the time on the way down?

b) How does the speed of the ball immediately after being shot compare with the speed when the ball returns to the same height as it was shot (on the way down)?

c) How do the corresponding velocities in (b) compare?

3) How is the change in velocity of a ball related to its acceleration and elapsed time?

4) How is the distance a ball travels related to its acceleration and elapsed time?

Apparatus:

• One meter stick

• a Nerf cannon and ball

• stop watch.

• digital camera & tripod

• Computer w/LoggerPro Software

Part 1: The Free Fall Model (from Galileo’s Equations)

Place the butt of the nerf cannon against the ground and point barrel as vertical as possible. Push the grip all the way forward, then pull it back toward the back grip to launch a ball. Use a stopwatch to measure the passage of time as the ball shoots from the cannon. You want to record the time for the ball to fly upward and return to the initial height of the gun barrel. Repeat for a total of 4 trials. Enter your data in the table below. Using a calculator, determine the average hang time. Warning: Do not shoot your classmates with the Nerf Cannon.

Using the equations above estimate the average muzzle velocity and the average height of the trajectory.

|Trial # |Hang Time (thang) | |

|1 | |{Estimated Values} |

|2 | |Avg. Muzzle Velocity (vmuzzle) |

|3 | | |

|4 | |Avg. Height (d) |

| tavg = | | |

Part 1: Video Analysis Verification

1. Position the Nerf cannon with its butt on the ground and aim it directly upward.

2. While recording with a digital camera, fire the Nerf cannon several times (BE SURE TO STABILIZE THE CAMERA WITH A TRIPOD). Stop recording when the last ball hits the ground. Be sure to include a “reference object” such as a meter stick in the field of view for scaling the movie.

3. Review the movie in the camera. If it is acceptable then connect the camera to a computer (via its USB cable) and upload the movie file to the “Desktop” for easy access.

4. Start-up LoggerPro software and open the “PHY101-VideoFreeFallAnalysis.XMBL” experiment file, located on the local network “I://HOME/” drive in the instructor’s 101 folder. Be certain to read the directions in the textbox (lower left hand window)

5. Insert your movie into the experiment by right clicking on the movie window (upper left hand window) then select BROWSE to locate your movie file.

6. Resize and move the movie field (if necessary) for viewability and convenience.

7. Use the QuickTime buttons to review the movie

a. Select the ball position in each frame during the fall

b. Scale movie using the “reference” object

c. Set origin to the top of the barrel Nerf cannon when the ball is fired (i.e. the point the projectile leaves the cannon)

Graphical analysis of free fall motion

8. Two graphs should be displayed in the main window, the position vs time graph and the velocity vs time graph for the fired Nerf projectile.

9. Use the Examine feature to determine the highest point during the projectile’s flight.

Maximum Height (1st ball): (don’t forget the units)

10. Use the Examine feature to determine the initial (muzzle) velocity of the fired projectile.

Muzzle Velocity(1st ball): (don’t forget the units)

11. Print out these graphs (you only need to do this for the first projectile)

12. Repeat this analysis, steps 6 through 10, for the other fired projectiles on your video. Be sure to “Clear All Date Points” before repeating.

13. Enter your values in Table 2 below.

14. Calculate the average muzzle velocity and maximum height for the nerf cannon using the data recorded in Table 2 below.

15. Calculate the % error between the estimated values calculated at the beginning of this experiment and the measured (video analysis) values. To calculate the % Error use the following equation:

[pic]

16. Record the % Error in Table 3 below.

|Table 2: Video Analysis of Nerf Cannon {Measured values} |

|Projectile # |Muzzle Velocity |Maximum Height |

|1 | | |

|2 | | |

|3 | | |

|4 | | |

|Average | | |

|Table 3: Summary of Results |

| |Average Measured Value |Average |% Error |

| |(Video Analysis) |Estimated Value | |

| | |(Calculation) | |

|Muzzle Velocity | | | |

|Maximum Height | | | |

Summary Questions:

1) Describe the position vs. time graph for fired projectile.

2) Describe the velocity vs. time graphs fired projectile.

3) Based on your video data, does the muzzle velocity depend on the order in which it was fired? Why or why not?

4) How precise are your calculated (estimated) results for muzzle velocity and height of projectile flight, respectively? What is the % range for each of these data sets?

5) How do your calculated results compare with those obtained from video analysis? Be specific.

6) Do your results support the assumption that air resistance is negligible during the projectile’s flight? Explain.

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