Measuring Height Indirectly Purpose: In this activity you will use your mathematics skills to indirectly measure the height of several objects. You will also practice percent error calculations. Materials: Protractor Meter stick String Laser pointer Procedure: 1. With a partner, obtain three pieces of string of different lengths. The string lengths should be roughly 2.5m, 3.3m, and 4.0m. 2. One person should hold an end of the first string to the top corner of one of the lab tables. Record the string length below. String 1 Length: 3. Pull the other end of the string so that it just touches the floor when held tautly. 4. Use a protractor to measure the angle between the floor and the string. Record below. String 1 Angle: 5. In the space below, draw a diagram of the right triangle created during the desk height measurement trial using string 1. Be sure to label the correct length and angle and indicate which component of the triangle is the unknown with a question mark. 6. Examine the diagram above to determine the correct equation to use, and then use your answers to steps 2 and 4 to calculate the estimated height of the desk using string #1. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units.
7. One person should hold an end of the second string to the top corner of the lab table. Record the string length below. String 2 Length: 8. Pull the other end of the string so that it just touches the floor when held tautly. 9. Use a protractor to measure the angle between the floor and the string. Record below. String 2 Angle: 10. Use your answers to steps 7 and 9 to calculate the estimated height of the desk using string #2. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 11. One person should hold an end of the third string to the top corner of the lab table. Record the string length below. String 3 Length: 12. Pull the other end of the string so that it just touches the floor when held tautly. 13. Use a protractor to measure the angle between the floor and the string. Record below. String 3 Angle: 14. Use your answers to steps 11 and 13 to calculate the estimated height of the desk using string #3. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units.
15. Use your answers to steps 6, 10, and 14 to calculate the average height of your three trials. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 16. Measure the actual height of the table and record below. Actual Desk Height: 17. Use your answers to steps 15 and 16 to calculate the percent error or your indirect desk height measurement. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 18. A properly formatted data table includes all data from the laboratory experiment, including calculated values and results. Complete the following, properly formatted data table by filling in the information from your indirect desk height measurement. String Length Angle Desk Indirect Height Calculated Height Average Height Actual Height Percent Error (m) ( ) (m) (m) (m) (%) 19. Hold the end of string 1 on the top of your forehead. Have your partner pull the other end of the string so that it just touches the floor when held tautly and use the protractor to measure the angle between the floor and the string. Record the string length and angle below. String 1 Length: String 1 Angle:
20. In the space below, draw a diagram of the right triangle created during your height measurement trial using string 1. Be sure to label the correct length and angle and indicate which component of the triangle is the unknown with a question mark. 21. Examine the diagram above to determine the correct equation to use, and then use your answers to step 19 to calculate your estimated height using string #1. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 22. Hold the end of string 2 on the top of your forehead. Have your partner pull the other end of the string so that it just touches the floor when held tautly and use the protractor to measure the angle between the floor and the string. Record the string length and angle below. String 2 Length: String 2 Angle: 23. Use your answers to step 22 to calculate your estimated height using string #2. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 24. Hold the end of string 3 on the top of your forehead. Have your partner pull the other end of the string so that it just touches the floor when held tautly and use the protractor to measure the angle between the floor and the string. Record the string length and angle below. String 3 Length: String 3 Angle:
25. Use your answers to step 24 to calculate your estimated height using string #3. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 26. Use your answers to steps 21, 23, and 25 to calculate your average height from the three trials. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 27. Measure your actual height and record below. Your Actual Height: 28. Use your answers to steps 26 and 27 to calculate the percent error or your indirect height measurement. Be sure to show all work, including givens and unknown, equation, substitution with units, and answer with units. 29. Use Microsoft Excel to create a properly formatted data table showing the information from the indirect height measurement of you. Include the data table by attaching it to this lab packet when submitting your work. 30. Using only a protractor, a meter stick, and a laser pointer, perform an indirect height measurement of one of the tall maroon cabinets in the room. Include all necessary, typed work by attaching it to this lab packet when submitting your work.
31. Calculate the percent error of your indirect cabinet height measurement. Include all necessary, typed work by attaching it to this lab packet when submitting your work. Questions: (Answer in written form below) 1. Based on your experimental results, is it possible to measure an object s height indirectly? 2. Why is step fifteen of the procedure experimentally important? 3. If you were by yourself and had only two meter sticks, explain how you might go about determining the height of a very tall tree without your feet having to leave the ground. 4. Identify two sources of experimental error within this activity and a possible solution for each. Note: No hypothesis or conclusion is required for this laboratory report.