In a region of space, the potential energy of the system varies with x as u = α − (βx − γ)2 , where α = 34 j, β = 1.0 j1/2m-1, γ = 12 j1/2, and x is measured in meters. a particle of mass m = 2.5 kg is initially at x0 = 11 m. assume there are no dissipative forces (friction, wind resistance, etc.) in this problem.

Consider a 1000 w iron whose base plate is made of 0.5 cm thick aluminum alloy 2024-t6 (ρ = 2770 kg/m3 and cp = 875 j/kg°c). the base plate has a surface area of 0.03 m2. initially, the iron is in thermal equilibrium with the ambient air at 22°c. assuming 90% of the heat generated in the resistance wires is transferred to the plate, determine the minimum time needed for the plate temperature to reach 200°c.