The magnetic flux through a metal ring varies with time t according to φb = 10 at^3 − 5 bt^2, where φ is in webers, a = 6.00 s^ −3, b = 18.0 s^ -2, and t is in seconds. the resistance of the ring is 5.00 ω. for the interval from t = 0 to t = 2.00 s, determine the maximum current induced in the ring.

Abeverage can is made of 3004-h19 aluminum alloy (elastic modulus 69 gpa, tensile yield strength 285 mpa, density 2.72 g/cm^3). the dimensions on the can are approximated as a thin-walled cylinder with a height of 4.83 inches, diameter of 2.60 inches. empty the can has a mass of 14.2 g. determine: a. the wall thickness of the cylinder b. assuming a pinned-pinned condition what is the critical load? c. assuming a fixed-fixed condition what is the critical load?