A skateboarder is practicing on the \"half-pipe\" shown in the figure below, usi
ID: 2144973 • 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.)
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.) If she starts from rest at the top of the half-pipe, what is her speed at the bottom? If the skateboarder has mass m = 53 kg, what is her apparent weight at the bottom of the half-pipe? What speed does she then have when she reaches the top edge on the other side of the half-pipe? Now suppose she has a speed of 12 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
a) (Potential energy at highest point) = (Kinetic energy at lowest point)
m g h = m v^2 / 2
v = sqrt (2 g h )
v = sqrt (2 * 9.8 * 4 )
v = 8.854 m/s
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b) At the bottom, centripetal acceleration is added to gravitational acceleration.
Ac = v^2 / r
Ac = 8.854^2 / 4
Ac = 19.6 m/s2
W = m * (Ac + g)
W = 53 * (19.6 + 9.8)
W = 1558.2 N
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c) By conservation of energy, all KE is converted to PE
her speed will be = 0 m/s
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4) (Potential energy at highest point) = (Kinetic energy at lowest point)
m g h = m v^2 / 2
h = v^2 / (2 g)
h = 12^2 / (2 * 9.8)
h = 7.35 m