Question

A truncated cone with a circular cross-section is suspended as shown and subjected to a force P. The Young’s modulus of the cone material is E, and the cross-sectional radius of the cone is given by the relation: rz r zL () 1 = ? o ( ) . Neglecting the weight of the cone itself, calculate the increase in length of the cone due to the applied force P.

Problem 1. (25 points): A truncated cone with a8886 circular cross-section is suspended as shown and subjected to a force P. The Young's modulus of the cone material is E, and the cross-sectional radius of the cone is given by the weight of the cone itself, calculate the increase in length of the cone due to the applied force P. 0.95L

Answer 1

r = r_0 (1 - Z/L) Now for element of length 'dZ' delta radius 'r' increase in length d delta = p dz/AE d delta = p times dz/pi r^2 E d delta = p/E pi times 1/r^2 (1 - z/L)^2 dz integral^delta_0 d delta = integral^0.952_0 p/Er^2_0 pi L^2/(L - Z)^2 dz delta s PL^2/pi E r^2_0 proportional [1/L - Z]^0.951_0 delta = PL^2/pi E r^2_0 times [1/L - 0.95 L - 1/L - 0] delta = PL^2/pi E r^2_0 times 19/L delta = 19PL/pi E r^2_0