Acceleration of Gravity on an Inclined Plane

Acceleration of Gravity on an Inclined Plane

Purpose: 1. To find the acceleration of gravity by studying the motion of a cart on an incline.
2. To gain further experience using the computer for data collection and analysis.

Equipment Needed: windows based computer with Logger Pro software, motion detector, ballistic cart,
aluminum track, wood blocks, meterstick, small carpenter level.

Procedure:
1. Connect labpro to computer and motion detector to DIG/SONIC2 port on labpro. Turn on the
computer and load the Logger Pro software by double clicking on its icon located within the Physics
Apps folder. A file named graphlab will be used to set up the computer for collecting the data needed
for this experiment. To open this file first select FILE/OPEN (with the mouse) and then open the
Mechanics folder by double clicking on its icon. When this folder opens, double click on graphlab
to open the file.
2. Incline the track slightly by putting the wood friction block under the track support at approximately
the 50 cm mark thus raising that end of the track. (The other track support should be near the
opposite end of the track.) Use a bubble level to make sure the track is reasonably level from side to
side. Adjust the leveling feet if necessary. Determine the inclination angle θ for the track by
carefully measuring the vertical and horizontal travel of the track (tan θ = Δy/Δx). Make a sketch in
your lab report showing your method of measurement of the angle of inclination.

                                                   method of measurement of the angle inclination for first trial
                                                   for angle 1.748

3. Place the detector at the upper end of the track facing down toward the lower end. Start with the cart
at the lower end of the track and give the cart a gentle uphill (toward the detector). Be sure to catch
the cart when it returns down the track to prevent damage to the cart or track. Take a few practice
runs so that the highest point of the cart's path brings it no closer than 50 cm from the motion
detector.
g sin θ =
(a1 + a2)
2
4. Start the computer taking data after the cart leaves your hand and observe both the position and
velocity graphs simultaneously by having two windows open—one above the other. Select suitable
scales for both vertical and horizontal axes to best show the motion. Be sure to properly label the
graphs with titles, units, etc. The graphs should yield smooth consistent curves. If not, repeat the trial
again. What type of curve do you expect to see for x vs t and v vs t?
i expect to see a negative slope curve for position vs time because the cart is going down the incline.
and for velocity vs time i expect to see a negative slopped straight line because it speeds up as it goes down on the track.

5. Find the accelerations, a1 and a2, of the cart by determining the slopes of the v vs t curve for each
portion of the motion (up and down). With the mouse, first select a range of times that represents the
motion going up the incline. Then choose ANALYZE/CURVE FIT and fit this portion of the
velocity curve to a linear function of time. The slope should be the acceleration a1. Similarly, repeat
the process by selecting a range of times representing the motion down the incline and thus determine
a2. Use the equation given in the introduction above to determine g.

                                        curve fit for the first trial at angle 1.748

6. Repeat at least two more trials for the same inclination. Average your values calculated for g and
compare your result with the accepted value: 9.80 m/s2.
7. Repeat the above experiment (steps 2, 5 and 6) for a larger value of θ by using a larger block of wood
to increase the angle of inclination of the track.
6. Show a representative set of data from one of your trials by obtaining a printout of the two graphs,
x vs t and v vs t. Show on the graph the time intervals used and the slope of the two different velocity
curves (up and down).

                                          the curve fit for all 3 trials on the position vs time graphs

                                          velocity vs time graph for all 3 trials

                                          the work done to get g sin of angle and comaring it to the accepted value of
                                          9.80 m/s^2
Errors: human errors in measuring and adjusting the track and the track and table not being fully labeled , also there could have been errors in movements when the motion detector was on that could have tainted the results.
conclusion: we learned how to find the acceleration of  gravity by studying the motion of the cart on the incline and after calculating these we find that its pretty close to the accepted value of 9.80m/s^2