Cycle II AP Physics
John Dewey High School
Problems in Elastic Deformation
Solve the following problems on a separate sheet of paper. Remember to employ proper problem-solving techniques throughout.
Equations and Physical Constants:
F/A = E([lfinal-loriginal]/loriginal) where F is applied force (N), A is effective cross-sectional area (mexp2), E is Young's modulus (N/mexp2), loriginal is
the original length of the body(m) and lfinal is the final length of the body (m).
F/A = S(dtangential/loriginal) where dtangential is the tangential displacement (m) and S is the shear modulus (N/mexp2).
Pfinal-Pinitial = B(-[Vfinal-Vinitial]/Vinitial) where Pfinal is final pressure, Pinitial is initial pressure (N/mexp2), B is the Bulk modulus (N/mexp2), Vfinal is the final volume and Vinitial is the initial volume (mexp3).
Young's Modulus for Bone (N/mexp2):
Tension: 1.6 x 10exp10 Compression: 9.4 x 10exp9
Bulk Modulus for Steel (N/mexp2):
1.4 x 10exp11
1 N/mexp2 = 1 Pa
1. Stretching, Compression, and Young's Modulus: Bone Compression. An acrobatic performer manages to support the combined weight of several colleagues with both legs. The combined weight amounts to approximately 1,640 N. Each thighbone (femur) of this performer possesses a length of 0.55 m and an effective cross-sectional area of 7.7 x 10exp-4 mexp2. Based on this information and your knowledge of elasticity, calculate the amount by which each thighbone compresses under the added weight.
2. Shear Deformation and the Shear Modulus: J-E-L-L-O. A rectangular block of Jell-O (a gelatin dessert) is resting on your horizontal dining room table. The block is 0.070 m long, 0.070 m wide, and 0.030 m thick. You are bored, impatiently waiting for dinner, and push tangentially (laterally) across the top surface of the block with a force of 0.45 N. The top surface moves a distance (dtangential) of 6.0 x 10exp-3 m relative to the bottom surface. Calculate the shear modulus of Jell-O.
3. Volume Deformation and the Bulk Modulus: The Mariana Deep-Ocean Trench. The Mariana trench is located in the southwestern Pacific Ocean, and at one place it is nearly seven miles beneath the surface of the water. The water pressure at the bottom of the trench here is enormous, being approximately 1.1 x 10exp8 Pa greater than the pressure at the surface. A solid steel ball possessing a volume of 0.20 mexp3 is dropped into the trench at this location and falls to the bottom. Calculate the change in volume experienced by the ball when it has reached the bottom of the trench.