The apparatus is initially at rest on a nearly frictionless surface. then you pull the string with a constant force f. at the instant when the center of the disk has moved a distance d, an additional length w of string has unwound off the disk. (use any variable or symbol stated above as necessary.)at this instant, what is the angular speed of the apparatus?

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 kn/m and is held by cables so that it is initially compressed 50 mm. knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.