Write your name, section, and today's date in the cell below:¶

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Synopsis¶

1. To learn:
2. Instruments to measure time, mass and length,
3. Physics in instruments beyond hand tools.
4. To do:
5. Use the provided hand tools to measure time, mass (weight) and length,
6. Research tools that measure nano meter or mass of atoms.

Purpose of this lab:¶

• Physics, which studies matter, energy and the interactions among them, is a science based on observations, measurements and modeling, in the language of mathematics.
• The ability to select and utilize the right instruments to conduct a measurement is essential in research and engineering. Above this is the understanding of the physics that empowers the instruments. This understanding leads to invention of new instruments which is the vanguard in advancing cutting-edge work.

Measurement in mechanics:¶

• The basic measurements are for time, mass and length.

Measurement in electromagnetism:¶

• Voltage, current, resistance

Time:¶

1) The physics used in a time measurement is to compare the duration against a known period (the unit time). Your watch has a mechanical pendulum or electrical oscillator plus a counting system, either mechanical or electrical. A wrist-watch provides a measurement precision of a second. A stop-watch goes down to 1/100 of a second or 10 milli-seconds ($10^{-3}$), which is the limit of human reaction time. There are instruments that measure to micro-($10^{-6}$), nano-($10^{-9}$) and pico-seconds ($10^{-12}$), or even higher precisions, depending on the oscillator the clock uses. 2) A time measurement (of a duration) is by definition relative (to the start time). If the reference serves all clocks, the measurements become absolute. A GPS receiver provides a PPS (pulse per second) signal that, with the other information the receiver sends out, offer an absolute time measurement with a precision of a microsecond. This is often used to compare events of a large scale experiment with sensors that are meters to kilometers apart.

Mass:¶

1) The definition of mass in physics is the quantitative measure of inertia, comes from Newton’s 2^nd Law of motion $\vec{F} = m\vec{a}$. On Earth, we usually associate mass with the weight of an object. One needs to remember that the weight of an object on Earth comes from the gravitational force on the object due to the mass of the whole planet Earth: $\vec{F}_g = m \vec{g}$, where $\vec{g}$ is the gravitational acceleration, 9.8 m/s at sea level and pointing to the center of the Earth. 2) In SI (International System of Units), the unit for mass is kilogram (kg) and it is a base unit. 3) To measure mass we usually use a scale or a balance. The physics employed in a scale can be either to compare the object with a known mass (example a chemical balance), or the signal that a sensor generates under the weight of the object (example a bathroom scale on a force sensor). Of course there are other ways to measure mass, for example, a mass spectrometer to measure the mass of atoms.

Length and coordinates in a reference system:¶

1) We compare the extent of an object with a known unit to measure its length. This unit length can be 1 millimeter (mm) on a tape measure, or 1 marking position on a micrometer (corresponding to 1 micron). We employ other physics principles to measure large or small distances, such as the distance to planets and stars, or the thickness of a film on a camera lens which is a few tens of nanometers. For small scales a tool that is often used is the interferometer which uses interference of two waves to do the measurement. 2) When you want to locate an object, a coordinate system must be defined. A city map is an example of a 2-dimensional coordinate system. A geographic coordinate system (GCS) of longitude, latitude and elevation is used to locate an object on the Earth. A GPS receiver sends out its coordinates every second. Coordinate systems commonly used in physics are Cartesian, cylindrical and spherical systems. The choice of coordinate system to utilize is often one of convenience, and conversions among coordinate systems are done using mathematical transformations. Physical phenomena are unaffected by the coordinate system we use to describe them.

Figure 1: Commonly employed measurement apparatus for length, mass, and time.

Procedure¶

Distance Measurement¶

• Let’s measure the length, breadth and width of the cuboid. Please report lengths, breadths and widths using all three kinds of rulers: A, B and C

Record your measurements of the dimensions of the cuboid here. Be sure to include units!¶

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Distance Measurement of an arbitrary shape¶

Let's take an arbitary shape like the one below:

Arbitrary distance or length measurement¶

• Find a way to measure the length
• Each of you should find a way to measure the length
• We will then make a histogram together
• If you feel like it, measure the distance with A, B and C rulers

Record your measurements here. Be sure to include units!¶

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Weight or mass measurement¶

Use the kitchen scale and the three-beam balance to measure the mass of the cuboid. How do the readings compare to the mass printed on the sample? Do these scales actually measure weight or mass?

Record your measurements here. Be sure to include units!¶

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Provide your resonses here¶

Time Measurement¶

A "g-ball" or "timing ball" with a built-in timer that starts when the ball is released and stops upon impact with a surface¶

• Decide on a certain height from which you will drop a timer ball or the g-ball.
• Use the tape measure to define distance and record the time
• Do this for a few measurements
• What do the values look like?
• Make a graph!

Record your measurements here. Be sure to include units!¶

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Let's look at other quantities of interest like voltage of a battery¶

Use the voltmeter to measure the voltage¶

Next week we will study oscilloscopes¶

Record your measurements here. Be sure to include units!¶

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