Question

**SEE FIGURE: http://www.webassign.net/ncsuplsemech2/8-post-006a.gif
Note: g = 32 ft/s2.
Part 1 - Estimate
(a) Estimate the maximum speed a rider might have at location .
16 m/s

(b) For the speed you estimated in part (a), using Conservation of Energy, determine the maximum height the rider can rise up to as he goes up the vert.
13.05 m

Part 2 - Calculations
(c) For the rest of this problem consider just the motion of the center of mass of the rider. Consider a standard half-pipe with h = 13 ft with a 4 ft vert. Consider a5.5 ft person whose center of mass is at his midheight. He starts from rest at location . What is his speed v2 at location if he does not crouch (his center of mass isat the same height relative to his feet)?

(d) Based on your answer in part (c) above, how high (what is the location of his center of mass relative to location ) will he go up the vert on the other side?

(e) If he wishes to go up beyond the edge of the vert, he will need to have greater kinetic energy when he is at location . To do this, the rider will pump as he goesback and forth on the half-pipe several times (he will crouch down as he approaches the flat to lower his center of mass) to further decrease his potential energy thenspring back up to convert his internal muscular energy to kinetic energy. Suppose the rider in this case wishes to rise above the edge of the vert so that the changein his center of mass position is 18 ft relative to the flat section of the pipe (location ), what speed does he need to have when he is at location ?

Answer 1

<p>b)at the bottom of the track velocity will be maximum,by conservation of energy.As the formula says, total energy at point (1) equals to totalenergy at point (2).</p>
<p>&#8756;&#160;mgh = 0.5mv²</p>
<p>&#8756;gh=0.5v²</p>
<p>&#8756;h=(0.5*v²)/(32/0.3) &#160; &#160; ....[ converting g fromft/s²&#160;to&#160;&#160;m/s²]</p>
<p>&#8756;h=(0.5*16*16)/(32*0.3)</p>
<p>&#8756;h=13.05 m</p>