A certain spring found not to obey Hooke's law exerts a restoring force Fx(x) = —ax — /3x2 if it is stretched or compressed, where a = 60.0 Him and /3 = 18.0 HIM2. The mass of the spring is negligible. (a) Calculate the potential-energy func-tion U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is at-tached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?

Alinearly polarized electromagnetic wave has an average intensity of 196 w/m^2. this wave is directed towards two ideal polarizers (in real polarizers, transmission is also effected by reflection and absorption). polarizer a is oriented with its transmission axis at an angle of θ_1=20.8∘ with the incident electric field. polarizer b has its axis at an angle of θ_2=63.0∘ with the incident electric field. what is the average intensity of the wave after it passes through polarizer a? what is the average intensity of the wave after it passes through polarizer b? suppose that the two polarizers a and b are interchanged. what would the average intensity be after passing through both polarizers?

Road users moving into your lane, brake lights, and abrupt changes in road surface are a. rare at night b. indicators of potential hazards c. not worth worrying about before you reach them d. no problem for experienced drivers

The air in an automobile tire with a volume of 2.60 ft3 is at 70°f and 21 psig. determine the amount of air that must be added to raise the pressure to the recommended value of 30 psig. assume the atmospheric pressure to be 14.6 psia and the temperature and the volume to remain constant. the gas constant of air is ru = 53.34ft⋅lbflbm⋅r(1 psia144 lbf/ft2) = 0.3704 psia⋅ft3lbm⋅r the amount of air that must be added to raise the pressure is lbm