A m = 8 kg block on a horizontal frictionless surface is att…

A m = 8 kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.85 kN/m).  The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown.  Starting from the “One Equation to Rule Them All” (the energy equation) and showing all steps, find the speed of the block when it is 13 cm from its equilibrium position.  (Round to nearest answer)

 A 2-kg ball slides on a curved wire, starting from rest at…

 A 2-kg ball slides on a curved wire, starting from rest at point A.  The segment from A to B is rough (i.e. it has friction!) and the segment from B to C is frictionless.  Find the speed of the ball at B if the ball comes to rest (momentarily) at C. (select closest answer)

A roller-coaster has a mass of 400 kg when fully loaded with…

A roller-coaster has a mass of 400 kg when fully loaded with passengers.  At the bottom of a circular dip of radius 60m (as shown in the figure) the car has a speed of 14 m/s.  What is the magnitude of the force of the track on the car at the bottom of the dip?

 (Extra Credit  worth 5 points):  All of the above objects h…

 (Extra Credit  worth 5 points):  All of the above objects have the same mass M, and the same radial distance R from the axis of rotation as shown.  Which two objects have the same moment of inertia about the central axis? (Select a correct answer and show work to prove why!)