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# Problem: A 20.0 kg wood ball hangs from a 2.10 m-long wire. The maximum tension the wire can withstand without breaking is 400 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

Let the mass of the wood ball to be M and the mass of the projectile to be m.

The maximum tension is then given as:

$\overline{){{\mathbf{T}}}_{\mathbf{m}\mathbf{a}\mathbf{x}}{\mathbf{=}}{\mathbf{\left(}}{\mathbf{M}}{\mathbf{+}}{\mathbf{m}}{\mathbf{\right)}}{\mathbf{g}}{\mathbf{+}}\frac{\mathbf{\left(}\mathbf{M}\mathbf{+}\mathbf{m}\mathbf{\right)}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{l}}}$

Substituting:

$\begin{array}{rcl}\mathbf{400}& \mathbf{=}& \mathbf{\left(}\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\right)}\mathbf{\left(}\mathbf{9}\mathbf{.}\mathbf{8}\mathbf{\right)}\mathbf{+}\frac{\mathbf{\left(}\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\right)}{\mathbf{v}}^{\mathbf{2}}}{\mathbf{2}\mathbf{.}\mathbf{0}}\\ \mathbf{v}& \mathbf{=}& \sqrt{\mathbf{18}\mathbf{.}\mathbf{5}}\end{array}$

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###### Problem Details

A 20.0 kg wood ball hangs from a 2.10 m-long wire. The maximum tension the wire can withstand without breaking is 400 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?

What scientific concept do you need to know in order to solve this problem?

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What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Staff's class at SJU.