PROBLEM 3. When a small correction 8U(r) is added to the potential energy U = -a!r, the paths of finite motion are no longer closed, and at each revolution the perihelion is dís- placed through a small angle 86. Find 8 when (a) &U = ß/r², (b) dU = x/2³

How much energy in terms of U is stored when spring is compress twice as much?

As shown in the figure below, two masses m, = 4.30 kg and m, which has a mass 60.0% that of m., are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m, and m, start from rest, after they have each traveled a distance h = 1.70 m, use energy content to determine the following. (a) speed v of the masses m/s (b) magnitude of the tension Tin the cord N

In 1953, the US Army field-tested the M65 Atomic Cannon, capable of firing a W9 warhead (364 kg) at a velocity of 333 m/s, whereupon it exploded with energy of 15 kilotons of TNT.  A) In the absence of air resistance, what is the optimal angle for firing the shell? Using your answer, how far would the shell travel? Assume the shell was launched and landed at the same height?   B) How long was the shell in the air?   C) What is the velocity (Magnitute and Direction) of the shell at the top of its trajectory?