# Problem: A 10.0 kg wood ball hangs from a 1.30 m-long wire. The maximum tension the wire can withstand without breaking is 600 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the largest speed this projectile can have without causing the cable to break?

###### FREE Expert Solution

If we let v0 be the velocity of the ball and the projectile, then we'll have:

$\begin{array}{rcl}\mathbf{T}& \mathbf{=}& \mathbf{\left(}\mathbf{M}\mathbf{+}\mathbf{m}\mathbf{\right)}\mathbf{g}\mathbf{+}\frac{\mathbf{\left(}\mathbf{M}\mathbf{+}\mathbf{m}\mathbf{\right)}{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}}{\mathbf{l}}\\ \frac{\mathbf{\left(}\mathbf{M}\mathbf{+}\mathbf{m}\mathbf{\right)}{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}}{\mathbf{l}}& \mathbf{=}& \mathbf{T}\mathbf{-}\mathbf{\left(}\mathbf{M}\mathbf{+}\mathbf{m}\mathbf{\right)}\mathbf{g}\\ {\mathbf{v}}_{\mathbf{0}}& \mathbf{=}& \sqrt{\frac{\mathbf{l}\mathbf{\left[}\mathbf{T}\mathbf{-}\mathbf{\left(}\mathbf{M}\mathbf{+}\mathbf{m}\mathbf{\right)}\mathbf{g}\mathbf{\right]}}{\mathbf{M}\mathbf{+}\mathbf{m}}}\\ & \mathbf{=}& \sqrt{\frac{\mathbf{\left(}\mathbf{1}\mathbf{.}\mathbf{30}\mathbf{\right)}\mathbf{\left[}\mathbf{600}\mathbf{-}\mathbf{\left(}\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{900}\mathbf{\right)}\mathbf{\left(}\mathbf{9}\mathbf{.}\mathbf{81}\mathbf{\right)}\mathbf{\right]}}{\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{900}}}\end{array}$

82% (470 ratings) ###### Problem Details

A 10.0 kg wood ball hangs from a 1.30 m-long wire. The maximum tension the wire can withstand without breaking is 600 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball.

What is the largest speed this projectile can have without causing the cable to break?