The sport of skateboarding provides an excellent example of theprinciple of Conservation of Energy. In particular, let us consider'vert skateboarding' where a person rides the skateboard on avertical ramp that forms part of a hemisphere referred to as a'half-pipe.' It consists of the transition from the curved part tothe flat and the vertical. Below is a schematic of a half-pipe withthe 'vert'. The surface of the half-pipe and the material of thewheels on the skateboard allow for an almost frictionless ride.Therefore we will neglect friction in the following analysis.
The rider starts from rest at location 1 at the edge of the in-rampand goes down the transition. Typically, as the rider approachesthe flat at location 2 he will crouch down to get his center ofmass as low as possible and thus increase his speed. To simplifythe problem, let us initially assume that the rider stays uprightas he goes down so that his center of mass location relative to hisfeet does not change from what it was at location 1 . In thefollowing problems, you can use the foot as the unit length insteadof meters. Note: g = 32 ft/s2.
Estimate the maximum speed a rider might have at location 2
(b) For the speed you estimated in part (a), using Conservation ofEnergy, determine the maximum height the rider can rise up to as hegoes up the vert.
The sport of skateboarding provides an excellent example of theprinciple of Conservation of Energy. In particular, let us consider'vert skateboarding' where a person rides the skateboard on avertical ramp that forms part of a hemisphere referred to as a'half-pipe.' It consists of the transition from the curved part tothe flat and the vertical. Below is a schematic of a half-pipe withthe 'vert'. The surface of the half-pipe and the material of thewheels on the skateboard allow for an almost frictionless ride.Therefore we will neglect friction in the following analysis.
The rider starts from rest at location 1 at the edge of the in-rampand goes down the transition. Typically, as the rider approachesthe flat at location 2 he will crouch down to get his center ofmass as low as possible and thus increase his speed. To simplifythe problem, let us initially assume that the rider stays uprightas he goes down so that his center of mass location relative to hisfeet does not change from what it was at location 1 . In thefollowing problems, you can use the foot as the unit length insteadof meters. Note: g = 32 ft/s2.
Estimate the maximum speed a rider might have at location 2
(b) For the speed you estimated in part (a), using Conservation ofEnergy, determine the maximum height the rider can rise up to as hegoes up the vert.
