Lab 1: Graphical Analysis
Stuart MacGillivray							February 22, 2002
Nicholas Levesque

Purpose: The purpose of this lab is to create graphs to determine the speed of a uniformly moving object, and the acceleration of a free-falling object.

Apparatus:  The items used were a sparktimer, two lengths of tickertape, some masking tape, a ruler, a motion cart, and a mass of 200 g.

Procedure:  See Handout.

Observations:

Time (s):	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
Distance (m):	0.027	0.054	0.080	0.108	0.137	0.164	0.192	0.220	0.248	0.276

1)  The graph appears to represent a straight line.  This indicates that the relationship between distance and time is a constant, and that there is a constant velocity involved.

Slope = Rise/Run
v= d/t

0.220 / 0.8 = 0.275

2)  The speed of the cart is roughly 0.275 m/s.

Slope = Rise/Run

0.075/0.083 = 0.9
0.238/0.083 = 2.87

3) The speed at 0.1s is 0.9 m/s, and the speed at 0.3s is 2.87 m/s.

Slope = Rise/Run

Rise = Y2 - Y1
2.87 - 0.9 = 1.97
Run = X2 - X1
0.3 - 0.1 = 0.2

1.97 / 0.2 = 9.85

4)  The slope of this graph will be 9.85 m/s/s.

vf = vi + at
vi = vf - at
0.9 - (9.85 * 0.1) = 0.050
2.87 - (9.85*0.1) = -0.085

5) The y-intercept of this graph will be near or equal to 0 m/s.

	Time t (s)		Distance d (m)		d/t (m/s)

	0.017			0.003			0.176
	0.033			0.010			0.303
	0.050			0.016			0.320
	0.067			0.027			0.403
	0.083			0.039			0.470
	0.100			0.054			0.540
	0.117			0.072			0.615
	0.133			0.093			0.699
	0.150			0.116			0.773
	0.167			0.142			0.850
	0.183			0.170			0.934
	0.200			0.201			1.01
	0.217			0.235			1.08
	0.233			0.271			1.16
	0.250			0.311			1.24
	0.267			0.353			1.32
	0.283			0.398			1.41
	0.300			0.446			1.49
	0.317			0.497			1.57
	0.333			0.550			1.65

Slope = Rise/Run

0.490/0.05 = 9.80

6) The slope of the graph is 9.80 m/s/s, and the y-intercept is 0.010 metres/second.

7)  The y-intercept is not 0 because the object was already moving when the first dots were marked.

%diff = (Theory - Experiment)/Theory * 100
(9.807 - 9.80) / 9.807 * 100 = 0.07% 

8) The acceleration of the mass was 9.80 m/s/s.  This is within 0.07% of the predicted total.

vf = vi + at
vf = 0.010 + (9.80 * 0.1) = 0.990

%diff = (|0.9 - 0.990|) / 0.9 * 100 =  10%
%diff = (|2.87 - 2.95|)/2.87 * 100 = 3%

9) The instantaneous speeds using this method were found to be 0.990 m/s at 0.1 seconds, and 2.95 m/s at 0.3 seconds.  These values are within 10% and 3% of the earlier values, respectively.

Discussion:

	The first difficulty in this experiment was accuracy.  The metre stick used had a smallest division of 1 mm, or 0.001 m.  Due to this, the distances read on the stick could not be read precisely enough.

	The second difficulty encountered was one of parallax.  It was very difficult to maneuver the metre stick to be directly next to the dots that were being measured.  In turn, this made the perspective of the measurer skew the distance readings one way or another.

	The third problem found in this experiment was control over the moving objects.  The motion cart went off at a slight angle, and the free-falling weight swung somewhat during its drop.  Due to this, the tickertape was not pulled through the sparktimer in a straight line; the dots on the tape swayed back and forth, once again skewing the data.

	The fourth problem encountered was the difficulty in pinpointing the start of the free-fall experiment.  Due to the sparktimer being on before the object was dropped, the start of the record was blurred beneath many dots.  This caused some complications with declaring where 0 was.

	The fifth problem found was limitations in data used.  The tickertape was somewhat short, causing an absence of data after a certain point.  This in turn made it difficult to find truly balanced averages, along with the earlier troubles in finding 0.

Conclusion:	The speed of the motion card was found to be 0.275 m/s.  The acceleration of gravity was found to be 9.80 m/s/s.  This latter value is within 0.07% of the predicted value.