- #1
danago
Gold Member
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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 traveling 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.
<br /> \begin{array}{c}<br /> E_M = E_k + E_p \\ <br /> = \frac{{mv^2 }}{2} + mgh \\ <br /> = 980J \\ <br /> \end{array}<br />
Since energy is conserved, i used this to calculate the tangental velocity at the bottom of the swing.
<br /> \begin{array}{l}<br /> 980 = 20v^2 \\ <br /> v = 7ms^{ - 1} \\ <br /> \end{array}<br />
Using this, i can calculate the centripetal force (net force).
<br /> \begin{array}{c}<br /> F_c = \frac{{mv^2 }}{r} \\ <br /> = 1633.\overline {33} \\ <br /> \end{array}<br />
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:
<br /> \begin{array}{c}<br /> \sum F = F - mg \\ <br /> F = \sum F + mg \\ <br /> = 2033.\overline {33} \\ <br /> \end{array}<br />
The answer the book gives is different however. I am not really sure what i have done wrong. Any help?
Thanks,
Dan.
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.
<br /> \begin{array}{c}<br /> E_M = E_k + E_p \\ <br /> = \frac{{mv^2 }}{2} + mgh \\ <br /> = 980J \\ <br /> \end{array}<br />
Since energy is conserved, i used this to calculate the tangental velocity at the bottom of the swing.
<br /> \begin{array}{l}<br /> 980 = 20v^2 \\ <br /> v = 7ms^{ - 1} \\ <br /> \end{array}<br />
Using this, i can calculate the centripetal force (net force).
<br /> \begin{array}{c}<br /> F_c = \frac{{mv^2 }}{r} \\ <br /> = 1633.\overline {33} \\ <br /> \end{array}<br />
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:
<br /> \begin{array}{c}<br /> \sum F = F - mg \\ <br /> F = \sum F + mg \\ <br /> = 2033.\overline {33} \\ <br /> \end{array}<br />
The answer the book gives is different however. I am not really sure what i have done wrong. Any help?
Thanks,
Dan.