Sam is an astronomer on planet hua, which orbits the distant star barnard. it has recently been accepted that hua is spherical in shape, although its exact size is unknown. while studying in the library, in the city of joy, sam learns that during equinox, barnard is directly overhead in the city of bar, located 1100.0 km north of his location. on the equinox, sam goes outside and measures the altitude of barnard at 67 degrees. what is the radius of hua in km?

Suppose you were asked to find the torque about point p due to the normal force n in terms of given quantities. which method of finding the torque would be the easiest to use?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 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. a) what is the block's initial mechanical energy? 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.

If the temperature were raised very high, classically what would we expect the heat capacity per object to be for this one-dimensional system? give a numerical value. chigh t = __ j/k/object (one reason for the discrepancy is that the high-temperature limit assumes that the number of oscillators is large (n > > 1), which is not the case in this tiny system.)