Problem: How far will a ball land from a table when launched from a known velocity?

PRELIMINARY QUESTIONS

1. If you were to drop a ball, releasing it from rest, what information would be needed to predict

how much time it would take for the ball to hit the floor? What assumptions must you make

The velocity, and the height of the drop.

2. If the ball in Question 1 is traveling at a known horizontal velocity when it starts to fall,

explain how you would calculate how far it will travel before it hits the ground.

I would use the formula vf = g * t

3. A pair of computer-interfaced Photogates can be used to accurately measure the time interval

for an object to break the beam of one Photogate and then another. If you wanted to know the

velocity of the object, what additional information would you need?

The direction of the object ,and the distance between the photogates.

Hypothesis: If gravity is normal power, then the ball launched from the ramp will land about 10 cm from the floor origin.

Materials:

Vernier Computer Interface Meter Stick

Masking Tape Logger Pro

2 Vernier Photogates Ramp

1 Marble Computer

Procedures:

Set up a ramp at an angle of about 10 degrees so that the ball will roll off, then roll about 10cm on the table and fall off. Connect the photo gates to DIG1 and DIG2. Then, set up the photo gates 8 to 10cm apart but still allowing the ball to roll through them when it goes off the ramp then falls off the table.

Make sure that the photogate plugged into DIG1 is closest to the ramp, but not on it. Mark a point on the ramp to roll the ball from each time. Roll the ball down the ramp, through the photo gates, and catch the ball before it hits the ground. Open the file 08 projectile motion on Logger Pro. Enter the distance in meters between the photogates. Measure this using a meter stick. Hit collect and roll the marble down the ramp to see if the photo gates are working. Hit stop. Then, hit “collect” and roll the marble down the ramp and through the gates ten times. After the tenth time hit “stop”. Look at the velocity table, It should read close to the same velocity each time. Measure the height of the table. Measure the spot on the floor directly below the point where the ball rolls off the table. Mark the point with masking tape. Use the formula to calculate the distance between where the ball will hit the ground and, the floor origin. Mark a prediction on the floor with masking tape. To account for the human factor, do the equation again using the minimum and maximum velocities. Release the ball and let it hit the floor, marking the impact point. Repeat 9 times. Enter the results in the data table.Results: The velocity was pretty constant during the tests. It was near .35- .4 m/s always. The range of the tests was .047 The median velocity is .383. There were two modes of .383 and .392 m/s There were no outliers in any of the tests.

Test | Velocity m/s |

1 | .350 m/s |

2 | .392 m/s |

3 | .392 m/s |

4 | .349 m/s |

5 | .383 m/s |

6 | .396 m/s |

7 | .383 m/s |

8 | .365 m/s |

9 | .358 m/s |

10 | .389 m/s |

The table height was a little more than ⅔ of a meter. My predicted impact point was short by 3 cm of the average. The impact points were close, never more than a centimeter off from the average. There were no outliers in any of the sets of data.

Maximum Velocity | .3967 m/s |

Minimum Velocity | .3497 m/s |

Average Velocity | .3793 m/s |

Table Height | 73.66.. cm |

Predicted Impact Point | 10 cm |

Minimum Impact Point Distance | 12 cm |

Maximum Impact Point Distance | 14 cm |

Actual Impact Point Distance | 13 cm |

ANALYSIS:

1. Should you expect any numerical prediction based on experimental measurements to be

exact? Would a range for the prediction be more appropriate? Explain.

No, any numerical prediction based on experimental measurements can not be

exact because the ball cannot be dropped from exactly the same spot each time due to the human factor. Therefore, a range would be better.

2. Was your actual impact point between your minimum and maximum impact predictions? If

so, your prediction was successful.

No, my impact prediction was unsuccessful because I predicted lower than the minimum impact point.

3. You accounted for variations in the velocity measurement in your range prediction. Are there

other measurements you used which affect the range prediction? What are they?

Air resistance and friction are other measurements that affect the range prediction.

4. Did you account for air resistance in your prediction? If so, how? If not, how would air

resistance change the distance the ball flies? I overestimated the affect of air resistance on the ball.

Conclusion:

I rejected my hypothesis of a 10 cm distance. The true result of 13 cm was 3 cm longer than my prediction of 10 cm. It did not work because I over estimated the affect of slowing air resistance on the marble.

There are two kinds of possible error. One is human error. For instance if the ball was dropped at a different point on the ramp, then the results would be different. Another possible error is mechanical error. If the photo gate malfunctioned, then the results would be different.

One different thing to test would be the affect of friction on an object over a lasting period of time. The photo gates would be setup 10 cm apart and then compare the data when they are setup 30 cm apart. The data would be analyzed for a change in velocity.

Through this lab, I was able to examine the affect of forces on the trajectory of a moving object. It also gave me experience using the photogate probe ware and more experience with logger pro. This will help me get a better understanding of the force of air resistance.