Another easy Conservation of Energy Question

[XxMuDvAyNexX]

A girl swings back and forth on a swing with ropes that are 4.00 m long. The maximum height she reaches is 2 m above the ground. At the lowest point of the swing she is .5 m above the ground. (a) The girl attains the maximum speed (1)at the top, (2) in the middle, (3) at the bottom of the swing. Why? (b) What is the girl's maximum speed?



I think 1/2mv^2=mghmax then the M would cancel leaving 1/2v^2=ghmax. Then I ended up with v=square root of 2ghmax.

Well using that equation I keep getting 3.13 m/sec for the lowest point(.5 m) and 6.26 m/sec for the highest point(2 m). The answers are the bottom since the lower the potential energy the higher the kinetic energy. And the other answer is 5.42 m/sec. I'm pretty lost on this one...

 

[lavalamp]

OK, hopefully you should be able to see the answer to part (a) right off the bat. At the top of the swing she has the most gravitational potential energy, and the lower she goes in the swing, the more of it is converted to kinetic energy.

Not all of it is converted though, because she's always at least 0.5m from the ground.

So her kinetic energy at the bottom of the swing is equal to the change in GPE.

Have another go now and see if you can get it.