   Chapter 7, Problem 28P

Chapter
Section
Textbook Problem

A snowboarder drops from rest into a halfpipe of radius R and slides down its frictionless surface to the bottom (Fig. P7.28). Show that (a) the snowboarder’s speed at the bottom of the halfpipe is v = 2 gr (Hint: Use conservation of energy), (b) the snowboarder’s centripetal acceleration at the bottom is ac = 2g, and (c) the normal force on the snow-boarder at the bottom of the halfpipe has magnitude 3mg (Hint: Use Newton’s second law of motion). Figure P7.28

(a)

To determine
The speed of the snowboarder at the bottom of the half line pipe is 2gR .

Explanation

Given Info:

The radius of the frictional less half line pipe is R.

Explanation:

Consider h=0 at the bottom of the pipe.

Since, the pipe is frictionless; according to conservation of energy,

(KE+PE)i=(KE+PE)f

Since, the snowboarder is at rest initially; the kinetic energy of the snowboarder is zero. The bottom of the pipe is considered as the h=0 point. Thus, the final potential energy of the snowboarder is zero

(b)

To determine
The centripetal acceleration of the snowboarder at the bottom of the pipe is,

ac=2g .

(c)

To determine
The magnitude of the normal force on the snowboarder at the bottom of the half pipe is 3mg .

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