A skateboarder goes over a hump in a road. The hump may be regarded as an arc of

ID: 1782941 • Letter: A

Question

A skateboarder goes over a hump in a road. The hump may be regarded as an arc of a circle with a radius of 11.0 m. (Disregard friction)

a) What speed is needed at the top of the hump for the normal force on the skateboarder to be zero?

[I thought it would be zero because I thought having a speed would've affected it.]

b) Layer, the skateboarder travels through a dip in the road. Can the normal force on the skateboarder be zero at the bottom of the dip? Explain.

[I said no. Don't remember why]

I got both of these problems wrong and now I want to know why and how.

forces at the top of the hump will be

weight - mg - acting downwards

normal reaction upwards

centripetal force away from the center = mv^2 / r

so mg - N - mv^2/r = 0

N = mg - mv^2/r

r = 11 m

now at the bottom of the dip the direction of centripetal force becomes in the same direction as mg = weight

mg + mv^2/r - N = 0

N = mg + mv^2/r