Assume that the cart is free to roll without friction and that the coefficient of static friction between the block and the cart is μs. derive an expression for the minimum horizontal force that must be applied to the block in order to keep it from falling to the ground. express your answer in terms of acceleration of gravity g and some or all of the variables m, m, and μs.

The friction of the water on a boat produces an acceleration of -10. m/s2. if the boat is traveling at 30. m/s and the motor is shut off, how long it take the boat to slow down to 5.0 m/s?

Mark creates a graphic organizer to review his notes aboutelectrical force.which labels belong in the regions marked x and y?

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.