What is the final velocity, in m/s, of a hoop that rolls without slipping down a 8.20 m high hill, starting from rest?

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.

Which statement is true? a) the work done to lift an object 6 meters is greater than the gravitational potential energy it gains. b) the work required to push an object is less than the work required to pull an object the same distance. c) the work required to raise an object to a height is equal to the gravitational potential energy the object gains. d) the work done against gravity to lift an object straight up is greater than the work required to roll it up a ramp.

Asquare isothermal chip is of width w=5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated; the front surface is exposed to the flow of a coolant at tinf=15 °c. from reliability considerations, the chip temperature must not exceed t=85 °c. if the coolant is air and the corresponding convection coefficient is h=200 w/m2 x k, what is the maximum allowable "power" of the chip? if the coolant is a liquid for which h=3000 w/m2 x k, what is the maximum allowable power of the chip?