(adsbygoogle = window.adsbygoogle || []).push({}); A 40kg gymnast is swinging on a horizontal bar. Her center of mass is 1.2m from the bar, and right at the top of the circle she is travelling in, her body has a speed of 1m/s.

What force must she hold onto the bar with right at the bottom of the swing if she is to continue swinging?

Well first thing i did was calculate the mechanical energy in the system right at the top of the swing.

[tex]

\begin{array}{c}

E_M = E_k + E_p \\

= \frac{{mv^2 }}{2} + mgh \\

= 980J \\

\end{array}

[/tex]

Since energy is conserved, i used this to calculate the tangental velocity at the bottom of the swing.

[tex]

\begin{array}{l}

980 = 20v^2 \\

v = 7ms^{ - 1} \\

\end{array}

[/tex]

Using this, i can calculate the centripetal force (net force).

[tex]

\begin{array}{c}

F_c = \frac{{mv^2 }}{r} \\

= 1633.\overline {33} \\

\end{array}

[/tex]

At the bottom of the swing, the force she holds on with and the weight force act in opposite directions, and i can say that:

[tex]

\begin{array}{c}

\sum F = F - mg \\

F = \sum F + mg \\

= 2033.\overline {33} \\

\end{array}

[/tex]

The answer the book gives is different however. Im not really sure what i have done wrong. Any help?

Thanks,

Dan.

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# Homework Help: Circular Motion

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