Newton's Law of Cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings (the ambient temperature). If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equal 0.5. Suppose the ambient temperature TA(t) is equal to a constant 95 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

Two resistors r1 and r2 may be connected either in series or parallel across an ideal battery with emf ε. we desire the rate of energy dissipation of the parallel combination to be 8.75 times that of the series combination. if r1 = 105 ω, what are the (a) smaller and (b) larger of the two values of r2 that result in that dissipation rate?

Which lists the pairs of plates in order from least to greatest in terms of the work done to move the electron?