A 55 kg skateboarder wants to just make it to the upper edge of a \"half pipe, \

Question

A 55 kg skateboarder wants to just make it to the upper edge of a "half pipe, " with a radius r, of 3.4 m shown in the figure below. What speed v_i does he need at the bottom if he is to coast all the way up? (a) First do the calculation treating the skateboarder and the board as a point particle, with the entire mass nearly in contact with the half-pipe. m/s (b) More realistically, the mass of the skateboarder in a deep crouch might be thought as concentrated 0.75 m from the half-pipe. Assuming he remains in that position all the way up, what v_i is needed to reach the upper edge? m/s

Explanation / Answer

here,
radius of half pipe, r = 3.4 m

mass of skater, m = 55 kg

part a:

From conservation of energy :
PE at top = KE at bottom
mg*r = 0.5 * m * v^2

Velocity, v = sqrt(2*g*h)
Velocity, v = sqrt(2*9.81*3.4)
Velocity, v = 8.167 m/s

Part b:
From conservation of energy :
PE at top = KE at bottom
mg*r = 0.5 * m * v^2

Velocity, v = sqrt(2*g*h)
Velocity, v = sqrt(2*9.81*(3.4 + 0.75))
Velocity, v = 9.023 m/s

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