Calculating Maximum Speed of a Child on a Swing | Simple Harmonic Motion

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To calculate the maximum speed of a child on a swing rising to a height of 0.5m, use the principle of conservation of energy. The potential energy (PE) at the height is given by the formula PE = mgh, where g is the acceleration due to gravity (10 m/s²). At maximum speed, this potential energy converts entirely into kinetic energy (KE), represented by KE = 0.5mv². By setting PE equal to KE, the maximum speed can be derived, which the book states is 3.2 m/s. The discussion clarifies that SHM equations are not applicable since only height is provided for this calculation.
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I don't find this topic too difficult but I am really stuggling on a question (im sure its really simple though)

A child on a swing rises throught a height of 0.5m. Ignoring resistive energy losses, calculate the maximum speed of the child (the child doesn't increase/decrease swing height and take g=10m/s/s)

Please could someone tell me the method and the answers you get. (the book says 3.2m/s but i didn't get that)

Thanks.
 
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Use conservation of energy.
 
oh, how would you do that ? I thought it was to do with the SHM equations.
 
The speed will be maximal when all of the original potential energy is converted to kinetic energy. The PE is given by mgh. The KE is 0.5mv^2.
You can't use the SHM equations here cause all you have is the height.
 

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