Problem 3: If a horizontal force P = 12 lb is applied to block , determine the acceleration of the block . Neglect friction. Hint: Acceleration of to the right and acceleration of upward, are ‘related’ to each other!

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.

According to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does maria's voyage take according to samir?

Using a caesar cypher with an offset of three characters (a -> d, b -> e, z -> c), what would be the correct cypher text for the plain text "attack at dawn"?