Final Exam Practice Solutions1. A ramp slopes upward to the right at 25 deg to the horizontal. Along the ramp is aspring with force constant 1300 N/m. A 15-kg block is pushed down the ramp into thespring, compressing the spring by 0.7 m. Upon being released from rest, the springdecompresses, releasing the block, which travels an additional 1.5 m up the ramp beforeflying in mid-air. The ramp is frictionless. The block leaves the ramp at a height of12 m above the ground below.(a) How far horizontally does the block travel before it hits the ground? (7.99 m)(b) What are the block’s final speed and direction when it hits the ground?(16.1m/s, 73.9 deg)1
2. An object has massM, radiusr, and moment of inertiaI=CMr2. Starting from restat an initial heighthabove the ground, the object rolls without slipping down a track.When the object reaches the ground, it enters the bottom of a circular loop-the-loopof radiusRL, rolling around the loop, and just barely making it over the top of theloop-the-loop.(a) From what initial height was the object released? Would a hoop or a solid sphererequire a greater initial height? ((b) What normal force does the object experience in the loop-the-loop when its dis-placement from the center of curvature makes an angle of 40 deg with the upwardvertical direction? Does a hoop or a solid sphere experience a larger normal force?