A skateboarder is practicing on the \"half-pipe\" shown in the figure below, usi

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) 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 = 56 kg, what is her apparent weight at the bottom of the half-pipe? N

(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

A.

using energy conservation

KEi + PEi = KEf + PEf

PEf = 0

KEi = 0

PEi = KEf

mgh = 0.5*mv^2

v = sqrt(2gh)

v = sqrt(2*9.81*4) =8.858 m/sec

B.

at the bottom ac will be added in ag

ac= centripetal acceleration

W = m*ac + m*g

ac = v^2/r

W = m*(ac + g)

W = 56*(8.858^2/4 + 9.81) = 1647.85 N

C.

v = 0 from energy conservation

because both are at same heights

D.

again

mgh = 0.5*mv^2

h = 0.5*15^2/9.81 = 11.46 m

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