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Lab 01

Measurements and Uncertainties

PHYS 111LV

Introduction/Background

The purpose of this lab is to introduce the concepts of measurement error and uncertainty. When making a measurement, we are limited by our apparatus to some maximum precision. So, when we measure a quantity, there is some uncertainty in the value of the quantity.

You will need download and read the reference handout for measurement error on blackboard. There you will find a full discussion on how to determine and report uncertainty in measured quantities. In this lab, we will be measuring the time it takes a mass to fall from a known height in order to determine the acceleration of the object due to gravity. This is a good experiment to demonstrate measurement error because it is very difficult to time how long it takes an object to fall from a few meters, due to human reflexes.

Based on Newton’s laws of motion, we can determine how far an object dropped from rest will fall in some amount of time. The equation is just

(1)

where h is the distance the object falls (the height it is dropped from), t is the amount of time it falls, and g is the acceleration due to gravity on the surface of the Earth. If h and t are measured in meters and seconds, then g is 9.8 m/s². In this lab, you will measure the time, t, it takes an object to fall from a known height, h, and calculate a value for g that will constitute your measured value for g.

Experiment

1) Measure the time it takes a marble to fall from a height of 1.5 meters using a stopwatch (you should have a ball bearing or marble in one of the bags in the lab kit, if you haven’t received a lab kit yet, improvise and report what you did, and any problems that arise).  Do at least 10 trials.  In your lab report, make sure you describe how you measured 1.5 meters and did the timing.

2) Determine g in terms of h and t using Eq. 1. (i.e. solve Eq. 1 for g).

3) Calculate g based on your measured values for h and t, and determine the uncertainty in g due to the uncertainties in h and t.

4) Repeat this experiment for 2.0 meters.

Notes

1. In your lab report

a. report your measured fall time for both 1.5 and 2.0 meters

b. report your measured value of g for both 1.5 and 2.0 meters

c. be sure to include your derivation for step 2

2. “Report” means write the average and uncertainty as x ± Δx with units

Questions

1. Do the two measurements you obtained for g using the 1.50 m and 2.0 m data “agree” (Hint: use the z’ mentioned in the uncertainty handout)?

2. The accepted value for g on Earth is 9.80 m / s². What is the percent error for each of you measured values?

3. Based on your data, can you say that the time it takes your ball bearing to fall from 1.50 m is less than the time it takes for it to fall 2.00 m?

4. Describe at least 2 ways you could change this experiment to improve your measured value for g.

5. Let’s say that after you did this experiment you found that you always stopped your stopwatch 0.3 s before the ball hit the ground (you anticipated accurately, something the human brain is inclined to do).  What type of error would this introduce into your experiment?