Answered: A snowboarder drops from rest into a…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section6.2: Circular Motion

Problem 14PP

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A snowboarder drops from rest into a halfpipe of radius R and slides down its frictionless surface to the bottom (see the figure below).

A halfpipe is depicted as the bottom half of a circle of radius R. A dashed line traces the path of a snowboarder, shown to enter the halfpipe from its top left edge. At the bottom of the halfpipe, an arrow labeled vector v extends from the snowboarder and points to the right.

Show that (a) the snowboarder's speed at the bottom of the halfpipe is

2gR,

(b) the snowboarder's centripetal acceleration at the bottom is

a_c = 2g,

and (c) the normal force on the snowboarder at the bottom of the halfpipe has magnitude

3mg.

A snowboarder drops from rest into a halfpipe of radius R and slides down its frictionless surface to the bottom (see the figure below).
R
Show that (a) the snowboarder's speed at the bottom of the halfpipe is v = V2gR, (b) the snowboarder's centripetal acceleration at the bottom is a. = 2g, and (c) the normal force on the snowboarder at the
bottom of the halfpipe has magnitude 3mg.
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