Imagine a 0.1-kg apple attached to a branch of a tree 2 m above a spring on the ground below. The apple falls and hits the spring, compressing it 0.1 m from its rest position. Now imagine if the compression is 0.36 cm. Is this spring stiffer or less stiff than the first spring?

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.

The mass of a bowling ball is 10 kg and the mass of a ping pong ball is 0.015 kg. if the two objects are 5 meters apart, what is the gravitational force ?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.