Physics Problems & Solutions: Classical Mechanics

The figure above shown a small mass connected to a string, which is attached to a vertical post. If the mass is released when the string is horizontal as shown, the magnitude of the total acceleration of the mass as a function of the angle θ is

A. $g \sin \theta$
B. $2g \cos \theta$
C. $2g \sin \theta$
D. $g\sqrt{3\cos^2\theta+1}$
E. $g\sqrt{3\sin^2\theta+1}$

(GR9277 #93)

Solution:

Total acceleration:

$\vec{a}=\vec{a}_{\text{tangential}}+\vec{a}_{\text{centripetal}}$

At initial position where $\theta=0$ , there is no string tension $\rightarrow \vec{a}_{\text{centripetal}}=0$

$\vec{a}=\vec{a}_{\text{tangential}}+0=\vec{a}_{\text{tangential}}=g$

Using method of elimination:

A. $g \sin \theta = g \sin 0=0 \rightarrow$ FALSE

B. $2g \cos \theta=2g \cos 0=2g \rightarrow$ FALSE

C. $2g \sin \theta=2g \sin 0=0 \rightarrow$ FALSE

D. $g\sqrt{3\cos^2\theta+1}=g\sqrt{3(1)+1}=2g \rightarrow$ FALSE

E. $g\sqrt{3\sin^2\theta+1}=g\sqrt{0+1}=g \rightarrow$ TRUE

Answer: E

Physics Problems & Solutions

Classical Mechanics - Pendulum

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