Accelaration due to Gravity

Purpose of the lab report: to report what you did, what you observed, and what it means.

Section Purpose

Abstract Answers the question: “What is a summary of what you did and what you found out?” (Write this last!)

Introduction Answers the question: “What was the motivation for this experiment and what broad strategy did you use?”

Methods Answers the question: “What exactly did you do?”

Experimental Setup

Describe your experimental set up, including each component and how you used it.

Precautions What lab precautions should be taken for this specific lab.

Data Answers the question: “What did you observe?”

Analysis Answers the question: “What do your observations mean?”

Assess Did you get results you expected from your understanding of theory and concepts? Did you get results that match standard values? Discuss what may have contributed to any deviation from standard values. Even if there were no deviation from standard values, explain what careful steps you took to get this result. This is a very important part of any experiment.

Sample Formal Laboratory Report with some of the information mentioned above

Checking the Speedometer of a Car

Alex Wong

9/25/2012

Abstract: The accuracy of a speedometer reading in a 1997 Toyota corolla was tested by

measuring the time it took the corolla to travel a range of distances (0-200m) when driven at a

constant speed of 100km/hr, as measured using the speedometer. The experimental speed

measurements were consistent with the speedometer reading. However, uncertainty in the

experiment was ±10.1%, so speedometer inaccuracies of 10% or less cannot be ruled out.

Introduction: I am often unsure of how reliable my speedometer is, so verifying its accuracy

could help me avoid costly tickets. We tested the accuracy of the speedometer in a 1997 Toyota

corolla by driving the corolla at a constant speed down a straight road and measuring the time it

took for the corolla to cover a range of distances.

Methods: A long straight stretch of road was identified near Largo MD. A traffic cone was

placed along the side of the road. A tape measure was used to measure distances 50m, 100m,

150m, and 200m along the road away from the cone, and cones were placed at each of these four

locations (Figure 1). Five stopwatches were coordinated to the nearest 1/100th of a second. Five

observers each took one of these watches and stood by each of the cones. A driver in the corolla

then drove the car along the stretch of road, maintaining a constant speed of 100km/hr according

to the speedometer. Each of the five observers noted the time when the car passed him or her.

Figure 1.

Data: The times recorded by each observer are reported in the table below:

Observer Location (±0.1m) Time (±0.25s)

Alex 0m 11:59:12.59

Beth 50m 11:59:14.67

Charlie 100m 11:59:16.05

Diana 150m 11:59:17.86

Ester 200m 11:59:19.85

The main factor causing uncertainty in the location measurements was the difficulty in stretching

the tape measure perfectly straight. The main factor causing uncertainty in the time

measurements were possibly varying reaction times of the observers.

The driver observed that the speedometer did not vary more than 2km/hr from 100km/hr during

the time in which she drove the car. Therefore the uncertainty in the speedometer reading was

±2km/hr.

Analysis:

In order to simplify our analysis we first define time t=0 to be the time the car passed the cone at

x=0m. Our time data was then expressed as the amount of time elapsed after the car passed the

first cone:

Observer Location (±0.1%) Time (±8%)

Alex 0m 0

Beth 50m 2.08

Charlie 100m 3.46

Diana 150m 5.27

Ester 200m 7.26

Percent uncertainty in the location is (±0.1m/100m)*100=0.1%. Percent uncertainty in the time

is (±0.25s/3.6s)*100=8%.

Since for an object moving with constant velocity x=x0+v*t, we expect that if we plot the

position vs. the time we will get a linear graph, and the slope of that graph will be the velocity of

the car. Figure 2 shows this graph.

Figure 2.

A linear regression of the data has an r2 value of 0.9965 indicating that the data is in fact quite

linear, confirming that the far was travelling at close to a constant velocity.

Using the regression equation we are able to find the explicit function for the position as a

function of time:

x = 28.1(m/s)*t - 1.68m

The slope of the regression line, 28.1m/s, is the experimental estimate for the speed of the car.

Since the uncertainty in the position is ±0.1% and the uncertainty in the time is ±8%, the

uncertainty in our experimental estimate for the velocity is 8 + 0.1 =8.1%, so our experimental

velocity is 28.1m/s ± 8.1%.

Our theoretical velocity, according to the speedometer, is 100km/hr ± 2km/hr = 100km/hr ± 2%

= 27.8m/s ± 2%.

The discrepancy between the speedometer measurement and the experimental measurement is

0.3m/s, or 100 * (0.3/27.8) = 1%. Our total uncertainty is 8.1% + 2% = 10.1%. Since the

discrepancy is less than the uncertainty, or experimental measurement of the speed of the car is

consistent with the speedometer value. However, this does not prove that the speedometer value

is accurate: our experimental design was expected to be accurate to only ±10.1%. Therefore, our

experiment could have detected speedometer errors of only 10.1% or greater. It is still possible

that the speedometer is inaccurate, but our experiment has shown that the speedometer is not

inaccurate by more than about 10%.

References:

1. Fredrick, Hans. “The accuracy of Vehicle Speedometers”.

http://www.ehow.com/info_12209329_accuracy-vehicle-speedometers.html. Accessed

9/25/2012.

y = 28.135x - 1.679 R² = 0.9965

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