Why is it important to know the center of gravity of an object?

Asmall metal bar, whose initial temperature was 10° c, is dropped into a large container of boiling water. how long will it take the bar to reach 70° c if it is known that its temperature increases 2° during the first second? (the boiling temperature for water is 100° c. round your answer to one decimal place.) sec how long will it take the bar to reach 98° c? (round your answer to one decimal place.)

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at 20â°c throughout the year, while the walls of the room are nominally at 27â°c and 14â°c in the summer and winter, respectively. the exposed surface of a person in the room may be assumed to be at a temperature of 32â°c throughout the year and to have an emissivity of 0.90. the coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 w/m2 â‹…â‹… k. what is the ratio of the thermal resistance due to convection to the thermal resistance due to radiation in the summer? what is the ratio of thermal resistances in the winter

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.