An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 39 . it has been determined that fracture results at a stress of 208 mpa when the maximum (or critical) internal crack length is 2.82 mm. a) determine the value of for this same component and alloy at a stress level of 270 mpa when the maximum internal crack length is 1.41 mm.

Aplane flying horizontally at an altitude of 1 mile and a speed of of 500mih passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it is 2mi away from the station.

1700 j of energy is lost from 0.14 kg object , the temperature decreases from 50°c to 45°c what is the specific heat of this object, amd what is the material ?

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.