A block whose mass is 5.7 kg slides on horizontal frictionless table top with a constant speed of 5 m/s. It is brought momentarily to rest by compressing a spring in its path. By what maximum distance is the spring compressed? (spring constant of spring, K = 1282.5 N/m)

A block of mass 2.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 470 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 13°.  a) The block, starting from rest, slides down the ramp a distance 54 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest?  b)  After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring?  c) What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?

10.

A spring with spring constant k has an unstretched length L . A block of mass m is pushed against the spring to compress it to the unknown position x = A. The block is not attached to the spring and the ground is frictionless. Another force acts on the block, attracting it to the point x = 0, with a magnitude c /x2, where c is a known constant. The block is released from rest. Obtain an algebraic equation for the compressed position x = A, such that the block escapes from the attractive force. (To escape means it will go all the way to infinity where it will have zero velocity.)