Lab 1 Essay

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Measurement and Experimental Error
Experiment #1

Tyler Brown
E01237083
Partner: Cameron Talbot
PHY 223
Lab Instructor: Ms. Shomsky
Tuesday, 9:00 AM-10:50 AM
Lecture Instructor: Dr. Behringer
Abstract
In this lab we took measurements using a ruler and Vernier calipers. We used these to obtain the density of our block, keeping the correct number of significant figures throughout. Two ways of measurement gave us different uncertainties, which we had to use to calculate our answer. We also took several measurements of a ball falling and obtained an average and a percent error. This lab taught us to keep significant figures and uncertainties throughout calculations.
Introduction
The purpose of this experiment was to maintain the right number of significant figures through calculations and being able to include uncertainties and use them in the calculations. We obtained a block of aluminum and found the properties of the block using a ruler, Vernier calipers and a mass balance. Using these measurements or dimensions we calculated the volume and density of our block. When taking these measurements we had to be careful and not carry too many digits in our calculations. We had to maintain the correct number of significant digits throughout our calculations. When calculating the volume we multiplied the length, width, and height together. V= L x W x H (1) Which when multiplying numbers together the rule for significant figures is the final answer will have the same number of significant digits as that with the least amount in the equation. This same rule applies for division which is used to find the density of the block. The density is the mass of the block, obtained through the mass balance, divided by the volume of the block. D = m/V (2) We were required to find two different densities, one with its uncertainties being independent and random and the other with them being not independent random. The equations for the were, D1= ((L/dL)2 + (W/dW)2 + (H/dH)2 + (M/dM)2)0.5 (3) D2= (L/dL) + (W/dW) + (H/dH) + (M/dM) (4) This would give us the information needed for part A of the lab, for part B we dropped a tennis ball several times, ten to be exact, and recorded the time it took to fall. Using a two meter stick we knew the height of the fall. We recorded the ball falling a total of ten times and used this to find the average. This would be the sum of all the times recorded divided by the number of drops, being ten. There also is an uncertainty with the time and the equation to find this is, Dt=((tmax-tavg)+(tavg-tmin))/2 (5) After we got t±dt, we needed to find the percent error using the calculated time to fall using the equation y=0.5gt2, solving for t. t= (2y/g)0.5 (6) Percent Error= ((tcalc)-(texp))/(tcalc) x 100 (7) This will give all of the information needed in this lab.
Results
We had to use a ruler and Vernier calipers to measure the dimensions of the block. We recorded the values into Table A. The uncertainties were given on these devices. Length Width Height

l
±δl
w
±δw
h
±δh

(m)
(m)
(m)
(m)
(m)
(m)
Ruler
0.0939
0.0005
0.0319
0.0005
0.0151
0.0005
Caliper
0.09414
0.00002
0.03286
0.00002
0.01692
0.00002

Using equation (1) and these values we found the volume of the block. Once we got the volume of the block and found the mass using the mass balance we recorded these values into Table A as well.
V = (0.0939m) + (0.0319m) + (0.0151m) = 0.0000452 m3
V = (0.09414m) + (0.03286m) + (0.01692m) = 0.00005234 m3
Mass

Volume
Density 1 Density 2 m
±δm

ρ
±δρ
ρ±δρ
±δρ
(kg)
(kg)
(m3)
(kg/m3)
(kg/m3)
(kg/m3)
(kg/m3)
0.1324
0.0001
0.0000452
2927
108
2927
161
0.1324
0.0001
0.00005234
2530
4
2530
7

After getting our volume and mass we used equation (2) to achieve the density of the block, one for the ruler and one for the calipers. This is when equations (3) and (4) are used to find the uncertainties of the density. They are Density 1 for equation (3) and Density 2 for equation
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