# PHY 1122 Lecture Notes - Lecture 5: Calipers, Length Measurement, Graduated Cylinder

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2 Mar 2015

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Simple measurements & buoyancy force

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Simple measurements & buoyancy force

Introduction

The purpose of this experiment is to practice basic experimental measurements, calculation techniques and result

presentation methods (tables, graphs, etc.) that will be useful during the whole semester. Most of the subjects

covered during this experiment are presented in the following tutorials:

Measuring techniques

Experimental errors

Propagation of errors

Repeated measurements

How to present a calculation example

How to prepare a graph

How to prepare a table

These documents are available in the Tutorial section at the BbLearn physics laboratory website. Students should

read these tutorials before coming to their lab session.

Part 1 – Length measurement

In this part, you will make length measurements using a meter stick and a vernier caliper. You will learn how to

report the uncertainty of your measurements and how to use them to perform error calculations when calculating

the density of some unknown materials.

Part 2 – Time measurement

For this part, you will carry out several time measurements of the period of oscillation of a pendulum. You will use

these repeated measurements to calculate statistical quantities such as the average, the standard deviation and

the standard error.

Part 3 – The buoyancy force

In this last part, you will investigate Archimedes’ principle which states that the buoyant force, 𝐹𝑏, exerted on an

object partially or fully submerged in a fluid will be equal to the weight of the fluid displaced by the object:

𝐹𝑏=𝜌𝑉𝑔 ,

(eq. 1)

where 𝜌 is the density of the fluid, 𝑉 is the volume of fluid displaced by the object, and 𝑔 is the gravitational

acceleration of 9.81 m/s2. You will use a suspended force sensor to measure the buoyancy force experienced by an

object that is gradually immersed in water. You will plot a graph of buoyancy force vs. the volume of displaced

liquid and, by using a linear regression tool, you will determine the value of the density of water, 𝜌.

Suggested reading

Students taking

Suggested reading

PHY 1122

Section 12.3

Young, H. D., Freedman, R. A., University Physics with Modern

Physics, 13th edition. Addison-Wesley (2012).

Simple measurements & buoyancy force

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Objectives

Part 1 – Length measurement

Familiarize yourself with different measuring instruments such as the meter stick and the vernier caliper.

Determine the uncertainty on each measurement and perform some error calculations based on length

measurements.

Prepare a proper table to report measurements.

Calculate the density of a metallic object and determine its metal types from a table.

Part 2 – Time measurement

Calculate the period of oscillation of a pendulum.

Calculate the average, the standard deviation and the standard error of several measurements.

Learn how to describe and account for variation in a set of measurements.

Learn how to describe a range of experimental values.

Part 3 – The buoyancy force

Determine the value of the density of a liquid using a force sensor to measure the buoyancy of an object

gradually being submerged in water.

Prepare a proper graph using Logger Pro and use the linear regression tool.

Compare your value with the accepted value for this quantity.

Materials

Meter stick and vernier caliper

Solid cylinder to measure the dimensions

Stopwatch

Pendulum

Electronic balance (one per classroom)

Computer equipped with Logger Pro and a Vernier computer interface

Force sensor

Lab jack with universal support and clamp holders

String and masses (2 x 200 g, 1 x 100 g)

Graduated cylinder

Safety warnings

Be careful not to drop the mass from the pendulum on your foot (you should always be wearing covered shoes in a

lab). Be careful to not spill water.

References for this manual

Density set. PASCO scientific (1992).