Unit 22: Tensile Stress & Strain
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q22.1) A rubber band (Young’s modulus 1.75 MPa) has a length of 10cm and a rectangular cross-section 2mm thick and 1cm wide. If you stretch the rubber band with a force of 25 N, by how many cm will it elongate?
*Q22.2) The rubber band from the previous question is hung from the ceiling. If a 1 kg mass is attached to its free end, by how many cm will it elongate?
***Q22.4) You wish to measure the Young’s modulus of a cylindrical piece of rubber of radius 1cm and length 30cm. To do this, you attach one end of the cylinder to the ceiling and attach progressively heavier masses to the free end, measuring the new length of the cylinder each time. Use the resulting data (shown below) to estimate the Young’s modulus of the rubber from which the cylinder is made. Note: to be a good experimentalist, you should make use of all the data (not just a single point).
**Q22.3) Two rubber bands are made of the same material and have the same cross-sectional area, but one is three-times the length of the other. You stretch both bands with the same force and find that the shorter of the two elongates by 5cm. By how many cm does the longer band elongate?