A skateboarder is practicing on the \"half-pipe\" shown in the figure below, usi
ID: 1585265 • Letter: A
Question
A skateboarder is practicing on the "half-pipe" shown in the figure below, using a special frictionless skateboard. (You can also ignore the kinetic energy of the skateboard's wheels.) 4.0 m (a) If she starts from rest at the top of the half-pipe, what is her speed at the bottom? m/s (b) If the skateboarder has mass m = 42 kg, what is her apparent weight at the bottom of the half-pipe? (c) What speed does she then have when she reaches the top edge on the other side of the half-pipe? m/s (d) Now suppose she has a speed of 15 m/s at the bottom of the half-pipe. What is the highest point she can reach? Hint: This point may be above the edge of the half-pipe. (Enter the distance from the bottom of the half-pipe.)Explanation / Answer
1)
(Potential energy at highest point) = (Kinetic energy at lowest point)
m g h = m v² / 2
so
v = (2 g h )
v = (2 9.8 4 )
v = 8.854 m/s
2)
At the bottom, centripetal acceleration is added to gravitational acceleration.
Ac = v² / r
Ac = 8.854² / 4
Ac = 19.6 m/s²
W = m (Ac + g)
W = 42 (19.6 + 9.8)
W = 1234.8 N
3)
By conservation of energy, all KE is converted to PE, so her speed will be 0 m/s
4)
(Potential energy at highest point) = (Kinetic energy at lowest point)
m g h = m v² / 2
so
h = v² / (2 g)
h = 15² / (2 9.8)
h = 11.479 m