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.
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.
graph 1graph 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
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.
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.
|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%