University Physics with Modern Physics (14th Edition)

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

Chapter 10 - Dynamics of Rotational Motion - Problems - Exercises - Page 329: 10.5

Answer

a) See picture. b) $-\boldsymbol{\hat{k}}$ (into the picture) c) $ \vec{\boldsymbol{\tau}} = (-1.05 \, \mathrm{Nm}) \boldsymbol{\hat{k}} $
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Work Step by Step

a) See picture. b) Right hand rule for $\vec{\boldsymbol{\tau}} = \vec{\boldsymbol{r}} \times \vec{\boldsymbol{F}}$: Place fingers in direction of $\vec{\boldsymbol{r}}$, then curl them towards $\vec{\boldsymbol{F}}$. Thumb is then in the direction of $\vec{\boldsymbol{\tau}}$, into the picture (in this case). c) $ \vec{\boldsymbol{\tau}} = \vec{\boldsymbol{r}} \times \vec{\boldsymbol{F}} = \big( (-0.450 \, \mathrm{m}) \boldsymbol{\hat{\imath}} + (0.150 \, \mathrm{m}) \boldsymbol{\hat{\jmath}} \big) \times \big( (-5.00 \, \mathrm{N}) \boldsymbol{\hat{\imath}} + (4.00 \, \mathrm{N}) \boldsymbol{\hat{\jmath}} \big) = \big( (-0.450 \, \mathrm{m})(4.00 \, \mathrm{N}) - (0.150 \, \mathrm{m})(-5.00 \, \mathrm{N}) \big) \boldsymbol{\hat{k}}= (-1.05 \, \mathrm{Nm}) \boldsymbol{\hat{k}} $ Negative $z$-direction means that the vector points into the picture, as predicted in b).
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