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AP® Physics C: Mechanics

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Panda-Lum: Determining When the Vine Will Break

APPHMC-4HKWYA

A large panda wants to swing on a vine, like Tarzan, creating a simple panda-lum. Unfortunately, the vine is too weak to handle the tension created by the panda.

The panda starts from a point that is directly horizontal with the point at which the vine is attached, with the vine outstretched to its full length $l$, so the vine makes an angle of ${90}^{\circ}$ with the vertical. The panda has mass $m$; the vine has a maximum tension equal to $T_{max}$.

What is the speed of the panda when the vine breaks?

A

$v=\sqrt {\cfrac {l{T}_{max}}{2m}}$

B

$v=\sqrt {\cfrac {2l{T}_{max}}{3m}}$

C

$v=\sqrt {\cfrac {l{T}_{max}}{m}}$

D

$v=\sqrt {\cfrac {2l{T}_{max}}{m}}$

E

$v=\sqrt {2gl}$