Amass m moves in a circular orbit of radius r0 under the inuence of a central force whose potential is given by where k is a positive constant and n is a positive integer. (a) determine the constraint on n that must hold for the particle orbit to be stable under small oscillations (i. e., the mass will oscillate about the circular orbit). (b) for n = 1, compute the frequency of small radial oscillations about this circular orbit.

The bar of prob. 5/82 is repeated here. the ends of the 0.4-m bar remain in contact with their re- spective support surfaces. end b has a velocity of 0.5 m/s and an acceleration of 0.3 m/s2 in the di- rections shown. determine the angular accelera- tion of the bar and the acceleration of end a.

Atank has a shape of a cone with a radius at the top of 2 m and a height of 5 m. the tank also has a 1 m spout at the top of the tank. the tank is filled with water up to a height of 2 m. find the work needed to pump all the water out the top of the spout. (use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)

An ascending elevator, hanging from a cable, is coming to a stop. part a part complete identify all forces acting on the elevator from the list below. select all that apply. select all that apply. kinetic friction normal force tension weight static friction submitprevious answers correct part b draw a free-body diagram of the object. draw the vectors starting at the black dot. the location and orientation of the vectors will be graded. the exact length of your vectors will not be graded but the relative length of one to the other will be graded.