4 16 Two soybeans are impacted against a steel surface

Last updated: 10/22/2023

4 16 Two soybeans are impacted against a steel surface Assume the impact is elastic and obeys the Hertz equations for contact between two solids This assumption is not valid Nevertheless insight can be gained by doing the analysis The equivalent radius of the first soybean is 0 251 cm and during the impact the maximum force reached is 22 1 N The equivalent radius is the radius of a sphere which has the same volume as the soybean The second soybean has an equivalent radius of 0 325 cm and during impact the maximum force reached is 37 0 N Assume the soybeans have the same modulus of elasticity 18 54 MPa and a Poisson s ratio of 0 35 For each soybean calculate the maximum normal stress developed during impact on the steel surface The maximum stress will develop at the point on the soybean where contact is first made between the soybean and the steel wall Compare the stresses experienced by the two soybeans Solution hints Assuming the soybeans are spherical calculate the radius of the contact circle a b from the force F and radius of the soybeans Then calculate the maximum contact stress Repeat the procedure for both small and large soybeans You will find that the stresses imposed on small and large soybeans are almost identical