Math Goal: Students will write the equation of a line using a line of best fit. Students will learn how to interpret the real life meaning of slope, y intercept, and equations.
CTE Goal: Students will become familiar with a torque wrench and learn the importance of torque.
Teacher notes and material needs are at the bottom.
Procedure:
1. Start the nut on the bolt and hand tighten.
2. Place the bolt and nut assembly in a vise. The vise should be clamped down on only the nut. Be sure the bolt can turn.
3. Place the protractor on the bolt. Using a marker, mark a line across the bolt head marking the 0 degree mark.
4. Set the digital torque wrench to its minimum torque setting in foot-pounds. Tighten the bolt. Record the amount of turn in degrees from 0 degrees and the digital torque wrench reading in foot pounds. This data point is marks the end of the ”snugging zone”. Compare how far you turned (degree) the bolt to someone else’s bolt. What can you determine about your grip strength? Be sure to label this point on the graph. Hint: Use a ruler to extend the line drawn on the bolt head to help read the protractor.
5. Increase the digital torque wrench setting by about 10 foot-pounds. Turn the bolt until the torque is reached. Record the amount of turn in degrees from 0 degrees and the digital torque reading. Note: the actual digital torque reading will be different than what you set on the wrench. Record the actual reading.
6. Repeat step 5 increases the digital torque wrench by 10 foot pounds each time. Continue increasing until you have material failure. This can look like a broken bolt, stripping metal, bolt turning in the vise, etc. Record this data point and label it as “material failure”. Create a data table with Degree Turn (X) and Foot-pounds (Y)
7. Graph your data.
8. Are there data points that do not fit the majority of the points?
a. If yes, give some reasons why these points do not fit the pattern.
b. What do you do with any points that do not fit the pattern?
9. Draw a line of best fit.
10. Calculate the slope of the line.
11. Calculate the y intercept
12. Write the equation of the line.
13. What is the real life meaning of:
a. Slope
b. Y intercept
14. What is the domain and range of this problem?
Materials Needed: For each group of students you will need: A 9/16” bolt (1 ½ “ long) and nut; digital torque wrench is needed and can be shared between 2 groups.; vise attached to table top; marker; ruler; protractor with a hexagon (size of bolt head) cut out of the center(see pattern at the end of document).
Teacher Notes:
This can be done with or without graphing calculators. Be sure to talk about the CTE situation so students can answer the question “Why do I care about this?”.
