The 9.3 kg object is released from rest at a height of 3.9 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant 613 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest.

Aballet student who learns with the of his instructor is demonstrating learning.

Acar drives toward the right over the top of a hill, as shown below. which arrow represents the centripetal acceleration? w x y z

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.