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From: Terminal Velocity Mission 1: Critical Measurements (pp: 32,33)
Stringing Along

In this field assignment, students examine the effect of temperature on the length of a measuring tape. They then create a length-measuring tool and analyze the effect of tension on the tool in order to make it more accurate.

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Stringing Along  

Matt Brumbelow and the team of argos at the Insurance Institute
for Highway Safety (IIHS)

Recall that your expedition goal is to understand the importance of accurate and precise measurements to help society. Now that you are fully briefed, it is time to apply your understanding of measurement to determine if certain measurement tools meet a specified requirement.

We often take for granted that the tools we use to measure objects are both accurate and precise. An error of one millimeter may not mean much in the classroom, but if it is your job to ensure that aircraft, like space shuttles and airplanes, are assembled correctly, one millimeter can cause losses of tens of thousands of dollars. In modern airplane building, the huge wings may be built in one factory, and other parts such as the body and the tail sections built in another. If the scientists, engineers, and technicians in different factories do not use the same unit of length, these expensive and critical parts may not fit together during assembly. Dan Sawyer and other engineers at NIST work hard to ensure that measuring instruments sold in the market are accurate.

Accurate measurements require accurate measuring tools, good measuring techniques, and a thorough understanding of what factors can affect measurements. In the case of measuring tapes, temperature and tension are two primary factors that affect the accuracy of measurements performed. Tapes expand or grow in length when their temperature increases and shrink when the temperature decreases. The amount of force or tension that is applied to the tape while it is in use can also make measurements less accurate. If a tape stretches due to tension, the distances between the graduations increase—making the tapes less accurate.

To begin this Field Assignment, you will examine the effect of temperature on the length of a measuring tape. Once you have completed your examination, you will create a length-measuring tool and analyze the effect of tension (expressed as a function of mass) on this tool in order to make it more accurate.


Materials

tape
Objectives

Field Preparation
  1. Using Dan Sawyer’s data found in the data sheet, graph length versus temperature of a 40-m measuring tape under constant tension. Add a line of best fit through the data points.
  2. Using the graph, estimate the length of the measuring tape at 10°C, 20°C, and 30°C.
  3. From the graph, describe how temperature affects the length of a measuring tape under constant tension.
  4. Describe how this may affect the construction of a building that takes place outside throughout the year in a location where the temperature fluctuates between -30º and 30ºC.
  5. Research the average temperature fluctuations in your area throughout the year and consider the effects on measurements in your region.
  6. Discuss with a classmate how construction workers might need to compensate for temperature fluctuations in your area.

Expedition Challenge
  1. Secure one end of a 50- to 75-cm piece of string to the table top edge with duct tape so the string hangs freely. Make sure the string is very secure and will not come loose when tugged.
  2. Make a mark on the string near where it is secured to the table. This will be the zero length mark on your measuring tool.
  3. With the string freely and loosely hanging down (straighten it just to make it taut, but do not pull on it), measure 30 cm down the string and mark it with your marker. This length measurement will be called 30 cm at zero tension.
  4. Tie the loose end of the string onto the hook of a spring scale or a 1,000 g mass.
  5. Apply tension by pulling on the other end of the spring scale until it reads 1,000 g, or by allowing the 1,000 g mass to hang down and pull on the string.
  6. Using a meter stick, measure 30 cm from the zero length mark on your string and make a mark. This measurement and tension will represent the standard for this experiment.
  7. Record the length at the following tensions (expressed as a function of mass):
    a. 250 g
    b. 500 g
    c. 750 g
    d. 1,250 g
    e. 1,500 g
    f. 1,750 g
  8. Graph your data, with tension on the x-axis and length on the y-axis. Plot your points and add a line of best fit for these data.
  9. Describe the effect of tension on the length measurement between the two points.
  10. Using the graph, determine the measured length under the following tensions (expressed as a function of mass):
    a. 350 g
    b. 1,650 g

    Expedition Debrief
    1. How did changes in tension affect your measurements?
    2. What impact could changes in tension have in the real world?
    3. What are some factors you need to take into account to make sure your measuring devices are accurate?

    Extension

    Experiment with different types of string to determine if they react the same under a variety of tensions.

    Journal Question

    Journal Question
    When analyzing measuring tapes, Dan Sawyer considers not only factors such as temperature and tension, but also what the tapes are made of (such as steel, iron, or gold) and how they were constructed. Describe some effects these variables could have on the construction of buildings, bridges, and cars, or on spacecraft.

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