A skateboarder with his board can be modeled as a particle of mass 77.0 kg, loca
ID: 2057676 • Letter: A
Question
A skateboarder with his board can be modeled as a particle of mass 77.0 kg, located at his center of mass (which we will study in a later chapter). As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point A). The half-pipe is a dry water channel, forming one half of a cylinder of radius 6.30 m with its axis horizontal. On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius 5.80 m.(a) Find his speed at the bottom of the half-pipe (point B).
m/s
(b) Find his centripetal acceleration.
m/s2
(c) Find the normal force nB acting on the skateboarder at point B.
N
Immediately after passing point B, he stands up and raises his arms, lifting his center of mass from 0.500 m to 0.970 m above the concrete (point C). To account for the conversion of chemical into mechanical energy, model his legs as doing work by pushing him vertically up, with a constant force equal to the normal force nB, over a distance of 0.470 m. (You will be able to solve this problem with a more accurate model described in a later chapter.)
(d) What is the work done on the skateboarder's body in this process?
J
Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.33 m. His body is horizontal when he passes point D, the far lip of the half-pipe.
(e) Find his speed at this location.
m/s
(f) At last he goes ballistic, twisting around while his center of mass moves vertically. How high above point D does he rise?
m
(g) Over what time interval is he airborne before he touches down, 2.14 m below the level of point D?
Explanation / Answer
x.......x