Sample Formal Laboratory Report for Physics on the Picket ...



Sample Formal Laboratory Report for Physics on the Picket Fence Lab without the parachute

Purpose:

The purpose of this experiment is to verify the acceleration due to gravity using the picket fence with a photogate, LabPro and LoggerPro software by measuring it with a precision of 0.5% or better.

Theory:

All objects, regardless of mass, fall with the same acceleration due to gravity assuming that there is no air resistance. Objects thrown upward or downward and those released from rest are falling freely once they are released. Any freely falling object experiences acceleration directed downward, regardless of the direction of its motion at any instant. The symbol “g” is used for this special acceleration at the Earth’s surface. The value of g is approximately 9.8 m/sec2. Since we are neglecting air friction and assuming that the free fall acceleration is constant, the motion of a freely falling object is equivalent to motion in one dimension under constant acceleration. Therefore the constant acceleration equations can be applied. Objects falling downward only under the influence of gravity can be graphically analyzed with a displacement versus time graph shown by a parabolic curve described in graph 1. This graph shows that as the object is falling, the displacement it travels each second is greater than the prior second. This graph can be mathematically illustrated by the equation

which is the equation for displacement as a function of time.

(y v

t t

graph 1 graph 2

Graph 2 shows the velocity as a function of time which is a linear relation for constant acceleration shown by the equation [pic]. Keeping acceleration constant, the graph of acceleration versus time would be a horizontal line at the value of acceleration.

Definition of symbols used:

t = time

vi = initial velocity

a = acceleration

(y = vertical displacement

vf = final velocity

g = acceleration due to gravity

Method:

1. Set up the photogate in a stand as shown below, connected to a LabPro which is connected to a PC. The photogate is attached to a ring stand to allow the picket fence to fall between the legs of the photogate.

[pic]

2. Open the loggerpro program, experiment 5 (picket fence) in the physics with computers file.

3. Hold the picket fence above the photogate so that it is oriented as shown above.

4. Click on Collect, when the collect button turns to Stop, drop the picket fence through the photogate—use a soft landing spot after the picket fence is clear. Be sure to drop it vertically and ensure it does not touch the photogate as it falls.

5. The computer will measure and graph the time it takes for each black line to pass through the photogate. A displacement versus time and velocity versus time graph will appear on the screen.

6. Click on the velocity versus time graph to activate it and then click on the linear fit button and include a best fit line to calculate the slope of the data. Record the slope in data table 1.

7. Do procedure 3-6 five more times.

8. Complete the rest of table 1.

Data Collected:

|TABLE 1—Velocity Versus Time Graph |

|Trial # | 1 |2 |3 |4 |5 |

|Slope |9.81 |9.79 |9.87 |9.76 |9.82 |

|Accel. “g” | | | | | |

|(m/sec2) |9.81 |9.79 |9.87 |9.76 |9.82 |

Average acceleration due to gravity, gavg = 9.815 m/s2 ( 0.055

Accepted acceleration due to gravity, gaccepted = 9.8 m/s2

Precision = 0.56%

Percent difference = 0.15%

Analysis of Data:

The value for part one trial number 3 is significantly higher than the other trials.

Part one calculations

Average acceleration: sum all 5 accelerations and divide by 5

( 9.81 + 9.79 + 9.87 + 9.76 + 9.82 m/s2) / 5 = 9.815 m/s2

Uncertainty: (maximum a – minimum a) / 2

(9.87 ( 9.76 m/s2) / 2 = 0.055 m/s2

Precision: [pic]

[pic]

Error calculation:

[pic]

Discussion:

The purpose of the experiment was to verify the acceleration due to gravity which was done with 0.15% error and 0.56% precision. Since both the error and precision are small, it shows that the experimental was fairly consistent and the average value is very close to the accepted value of acceleration due to gravity. Since the picket fence fell through a short distance close to sea level, the acceleration due to gravity remained constant throughout the entire fall through the photogate. Each equidistant black line on the picket fence passed through the gate in shorter and short time increments because it was accelerating, resulting in the graphs used to collect the data.

Air resistance did have an effect on the falling fence but it was so minute, it did not affect the data. If air resistance was large enough to affect the data, the acceleration due to gravity would be less than 9.8 m/sec2. Performing this experiment in a vacuum would eliminate the error due to air resistance, but both the experiment results and limitations of the lab equipment show it is an unnecessary improvement. Other things that could cause a change in experimental value of acceleration would be if the fence fell crooked or was pushed down slightly. If the photogate fell crooked it would cause a slight decrease in distance between black lines ultimately causing a change in acceleration. Having the fence short keeps that error minimal. A reading such as part 1 trial 3 (9.87) which is above the actual value of g indicates there may have been a minor problems with this drop. Proper dropping technique will minimize many errors associated with this lab. An automated dropping device would significantly improve the precision of this lab. Equipment measurement precision does not have much affect on error because the computer can record to many decimal places—depending on how it gets set by the user.

Ultimately, the laboratory was partially successful in verifying the acceleration due to gravity given the low percent error comparing to the accepted value, however the objective to measure g to a precision of 0.5% was not achieved. When trial 3 is removed and the precision is recalculated, the objective is achieved. Based on this, the experiment results could be improved by performing the experiment again with an improved method for dropping the picket fence and more trials.

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[pic]

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