Acceleration of Gravity on an Inclined Plane (09-04-12)

Purpose:

The purpose of this lab was to find the acceleration of gravity by studying the motion of a cart on an incline while gaining further experience using the Computer for data collection and analysis.
This lab can be found at http://www.hartnell.edu/physics/labs/4a/4accelerationofgravityinclined.pdf

Experiment

Data Collected from a cart on an inclined plane using 2 different angles
Equation for acceleration (gravity) along inclined plane:
gsinѲ=(a1+a2)/2
Scenario 1	sinѲ=5.9/210		Ѳ=1.61°
measured values	a1	a2	gexp	% difference
take 1	0.304	0.251	9.877	0.787
take 2	0.316	0.217	9.486	3.208
take 3	0.322	0.232	9.859	0.605
Average	na	na	9.741	0.605
Scenario 2	sinѲ=20.9/210		Ѳ=5.71°
measured values	a1	a2	gexp
take 1	0.988	0.929	9.631	1.726
take 2	0.981	0.908	9.490	3.161
take 3	0.985	0.926	9.601	2.033
Average	na	na	9.574	2.307

Below are 2 views of the same velocity vs time graph showing the slope (acceleration) for the trip up the ramp and then down the ramp respectively. Note: our measurement unit (sonar detector) is calibrated such that movement towards it is given a  negative value while movement away a positive one. Our unit was placed at the top of the inclined ramp and the cart was slid up before traveling back down. In both graphs below the line is the important feature (the dip before represents velocity changing due to external thrust by my hand, the dips and bounces after wards represent the effect of my hand stopping the cart).

Measuring velocity as cart rises up track

Measuring velocity as cart rolls back down track

Below is our graph of position vs time. the entire parabola is important the shaded grey area was not important in this lab

position vs time graph

Below is a crude drawing of our set up

Conclusions:

The graphs of velocity and graphs of position are consistent with what should be expected. The velocity graph should be a straight line, while position graph a parabola. In this experiment gravity was able to be measured at 9.7 meters per second per second. With numerous sources of error the error percentage was .6 of a percent from the actual value of gravity (9.8 meters per second per second). One interesting source of error was the meter stick, with millimeter marks on it it is better for larger measurements that smaller ones. More accuracy should be expected on the larger angle experiment, however this one had the largest percent difference of error. This may be because in fact while the side next to the motion detector was higher the side behind the cart was actually lower. Other sources of error came from the push on the cart. When a human hand is involved it is impossible to slide it up with the same forces every time. The hand and person tossing the cart can also get picked up by the motion detector interfering with the accuracy. For increased accuracy further experiments could use some mechanical way of launching the cart up the track. Also permanently attaching the motion detector instead of just letting it rest on the track might also increase accuracy. Finally by using a perfectly level table as a starting spot and with a more accurate way of measuring the angle of the track, perhaps a surveyor's theodolite the percent difference could be improved.

Lab 2 Acceleration of Gravity 08-28-12

The lab is found here
http://www.hartnell.edu/physics/labs/4a/2accelerationofgravityrubberballv2.pdf

#4 Why should the graph of position over time be a porabola for a ball tossed up and allowed to fall?
An observer of the ball would notice how smothly the ball transitions from movement to stop to movement in the oposite direction. A porabola decribes the motion of the ball over time. first moving (up) rapidly, slowing down, freezing (stopping), then slowly (falling down) finally picking up speed (falling) before reaching it original position. A porabola is merily the mathmatical way of descibing the balls motion.

#5 Table computed using experimented measurements and percent error equation
percent error=((measured-actual)/actual)*100%
actual for this experiment was 9.80m/s^2

Results from Falling Body Experiments
Trial	gexp (2A) (m/s2)	% Difference	gexp (m) (m/s2)	% Difference
1	-9.7	1.0	-9.9	1.0
2	-9.6	2.0	-10.1	3.0
3	-9.5	3.0	-9.9	1.0
4	-9.4	4.0	-9.0	8.0
5	-9.7	1.0	-9.6	2.0

There was some confusion as to significant figures steming from not reading the instuctions acurately enough leading to assuming that gravity was 9.8m/s^2; that is the reason for only 2 decimal places in the answers.

#6

Above is the graphs of position vs. time and velocity vs. time
The velocity graph for all 5 cases where velocity is positive; the ball is moving up. Where velocity reaces the y axis (y=0) the ball has reached the maximum hight and stopped moving. When velocity is negative the ball is falling down. The curve or line rather is negatively sloped because during that time is is being acted upon by gravity in the oposite direction of being thrown up. Hence it is slowing down after being tossed up and speeding up as it falls This graph represents how gravity is affecting the velocity of the ball.

Conclusions:
For balls tossed up and allowed to fall back down the graph position vs. time will be a porabola, the graph velocity vs. time will be a sloped line in the negative direction.
Significant digits are significant.