PURPOSE: To examine the validity of the statement:
In the absence if all other external forces except gravity,
a falling body will accelerate at 9.8m/s^2.
a falling body will accelerate at 9.8m/s^2.
(Determination of g)
"Demonstrate the motion of a freely falling body, determine g, and study the basic laws of motion with our well-known apparatus. The sturdy column provides a long 1.5 meter falling distance for an accurate reading. When the free-fall body, held at the top by an electromagnet, is released, its fall is precisely recorded by a spark generator. The marks made at intervals on the spark-sensitive tape attached to the column give students can then calculate acceleration. The apparatus comes with a heavy tripod base with leveling screws, a free-fall body, a weighted clip to anchor the spark paper, an electromagnet with power supply ... A spark generator and tape are needed. Overall height of apparatus is 1.86 meters."
- Turn the dial hooded up to the electromagnet up a bit.
- Hang the wooden cylinder with the metal ring around it (found at the bottom of the apparatus on the electromagnet.
- Turn on the power on the sparker.
- Hold down the spark button on the sparker box. (This starts sparking at 60 Hz. The spark leaves a dot on the paper.)
- Turn the electromagnet off so that the cylinder piece falls.
- Turn off the power to the sparker.
- Tear off the paper strip.
The result is a piece of tape with dots corresponding to the position of the falling mass every 1/60th of a second:
We measured the distance between each of the dots and plotted them with an Excel sheet.
The beginning of the experiment is shown at the top with t = 0 and distance = 0 (origin) with each new row the time advanced 1/60th of a second. This spreadsheet allowed for us to calculate the change in position between each dot. The Mid-Interval column represents the time for the middle of each 1/60th second interval. Because we found Δx and Δt we were able to find and plot the Mid-Interval Speed.
Using a new sheet we plotted the mid-interval speed.
To show that, for constant acceleration, the velocity in the middle of a time interval is the same as the average velocity for that time interval, we simply use the kinematic equations.
For the average velocity, we can use the definition (V=Δx/Δt) and for the velocity in the middle of the interval we use Δx=(1/2)*(V.initial + V.final)*t and choosing specific mid-interval speed values for the final and initial velocities.
To find the acceleration from the graph, we added a Trendline on the graph and with the equation in slope-intercept form, we were able to easily find the acceleration. The slope of the Trendline represents the acceleration. The acceleration of gravity we found through the graph's slope was 939cm/s^2.
Although we used efficient computer programs to calculate certain values, there is still a certain level of uncertainty accompanied with our calculated values.
The expected value to obtain for the acceleration of gravity is 9.81m/s, yet our calculations show that the value is 9.39m/s. The error(s) made could possibly have been the neglecting of air resistence, friction in the apparatus and also maybe some unknown mistakes.
Below is a chart with data from multiple groups performing identical experiments. The deviation from the actual value for gravity to the calculated value is displayed and after finding the absolute value of each given deviation value we were able to find the average deviation for all the groups.
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