University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 3 - Motion in Two or Three Dimensions - Problems - Discussion Questions - Page 92: Q3.1

Answer

The acceleration is tangential at the midpoint it is radial . At the points in between both radial and the tangential component of acceleration is non-zero.

Work Step by Step

The Mass travels in an arc of a circle. So there is a radial acceleration which is : $a_{rad}=\frac{v^{2}}{R}$ (3-28) At the endpoint, Its speed is zero and when v = 0 and $a_{rad}=0$ . Something [the tangent component of acceleration] causes the Speed to changed from zero. Thus at the end of Swing, the acceleration is tangent to the arc of Swing and directed towards the midpoint at the midpoint. At the point the speeds of the mass are maximum. There is radial acceleration $a_{rad}=\frac{v^{2}}{R}$directed upward . Since the speed is maximum, [the slope of the v-t graph is zero] $\frac{dv}{dt}=0 and a_{tan}=0$ At the midpoint, the acceleration is radially upward The conclusion : In the end, the acceleration is tangential at the midpoint it is radial. At the points in between both radial and the tangential component of acceleration is non-zero.
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