Answer to Question #189466 in Civil and Environmental Engineering for LIT JOLLY

Question

A horizontal arm, capable of rotation about a vertical shaft, carries a mass of 2.5 kg, bolted to it by a 1 cm bolt at a distance of 50 cm from the axis of the shaft. The axis of the bolt is vertical. if the ultimate shearing strength of the bolt is 50 MN/ m ², at what speed will the bolt snap?

Answer 1

Total force is the sum of weight due to gravity and centripetal force acting

Total force= Ultimate shear stress of bolt x cross section area of bolt

=50*10^6*3.14*(1/100)^2/4

=3925N

Weight due to gravity=m*g=2.5*9.81=24.52N

Centripetal force=mv^2/r=2.5*(v^2)/0.50

=5v^2

Thus,

3925=24.52+5v^2

(3925-24.52)/5=v^2

v=√780.096

v=27.93m/s